diff --git a/DESCRIPTION b/DESCRIPTION
index 9c2fa2b6..bbb76bc6 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,6 +1,6 @@
 Package: dials
 Title: Tools for Creating Tuning Parameter Values
-Version: 1.4.2.9000
+Version: 1.4.2.9001
 Authors@R: c(
     person("Max", "Kuhn", , "max@posit.co", role = "aut"),
     person("Hannah", "Frick", , "hannah@posit.co", role = c("aut", "cre")),
diff --git a/NAMESPACE b/NAMESPACE
index b794e52a..a9324c67 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -129,6 +129,8 @@ export(num_random_splits)
 export(num_runs)
 export(num_terms)
 export(num_tokens)
+export(odds_link)
+export(ordinal_link)
 export(over_ratio)
 export(parameters)
 export(parameters_constr)
@@ -206,6 +208,8 @@ export(values_activation)
 export(values_cal_cls)
 export(values_cal_reg)
 export(values_initial_umap)
+export(values_odds_link)
+export(values_ordinal_link)
 export(values_prune_method)
 export(values_regularization_method)
 export(values_scheduler)
diff --git a/NEWS.md b/NEWS.md
index b9e49d5c..2d269989 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,5 +1,7 @@
 # dials (development version)
 
+* `ordinal_link()` and `odds_link()` are two new parameters for the new `ordinal_reg()` models in parsnip (@corybrunson, #435).
+
 * A bug was fixed where some space-filling designs did not respect the `original` argument (#409).
 
 * Parameters were added for the `tab_pfn` model: `num_estimators()`, `softmax_temperature()`, `balance_probabilities()`, `average_before_softmax()`, and `training_set_limit()`.
diff --git a/R/param_ordinal_link.R b/R/param_ordinal_link.R
new file mode 100644
index 00000000..c15a0439
--- /dev/null
+++ b/R/param_ordinal_link.R
@@ -0,0 +1,60 @@
+#' Ordinal Regression Link Functions (character)
+#'
+#' The ordinal and odds link functions of an ordinal regression model.
+#'
+#' @param values For `*_link()`, a character string from among the possible
+#'   values encoded in `values_*_link`. See the examples below.
+#'
+#' @details These parameters are used by ordinal regression models specified by
+#'   `parsnip::ordinal_reg()`, for example `parsnip::set_engine('polr')`. The
+#'   nomenclature is taken from Wurm et al (2021), who characterize the pair of
+#'   functions as a composite link function. Note that different engines support
+#'   different subsets of link functions.
+#'
+#' @references Wurm, Michael J., Rathouz, Paul J., & Hanlon, Bret M. (2021).
+#'   Regularized Ordinal Regression and the ordinalNet R Package. _Journal of
+#'   Statistical Software_, 99(6), 1–42. 10.18637/jss.v099.i06
+#' @examples
+#' values_ordinal_link
+#' ordinal_link()
+#' values_odds_link
+#' odds_link()
+#' @export
+ordinal_link <- function(values = values_ordinal_link) {
+  new_qual_param(
+    type = "character",
+    values = values,
+    label = c(ordinal_link = "Ordinal Link"),
+    finalize = NULL
+  )
+}
+
+#' @rdname ordinal_link
+#' @export
+values_ordinal_link <- c(
+  "logistic",
+  "probit",
+  "loglog",
+  "cloglog",
+  "cauchit"
+)
+
+#' @rdname ordinal_link
+#' @export
+odds_link <- function(values = values_odds_link) {
+  new_qual_param(
+    type = "character",
+    values = values,
+    label = c(odds_link = "Odds Link"),
+    finalize = NULL
+  )
+}
+
+#' @rdname ordinal_link
+#' @export
+values_odds_link <- c(
+  "cumulative_link",
+  "adjacent_categories",
+  "continuation_ratio",
+  "stopping_ratio"
+)
diff --git a/_pkgdown.yml b/_pkgdown.yml
index d1ec29a2..d5494ff6 100644
--- a/_pkgdown.yml
+++ b/_pkgdown.yml
@@ -84,6 +84,7 @@ reference:
   - num_comp
   - num_estimators
   - num_knots
+  - ordinal_link
   - penalty
   - predictor_prop
   - prune_method
diff --git a/man/ordinal_link.Rd b/man/ordinal_link.Rd
new file mode 100644
index 00000000..058f7340
--- /dev/null
+++ b/man/ordinal_link.Rd
@@ -0,0 +1,49 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/param_ordinal_link.R
+\docType{data}
+\name{ordinal_link}
+\alias{ordinal_link}
+\alias{values_ordinal_link}
+\alias{odds_link}
+\alias{values_odds_link}
+\title{Ordinal Regression Link Functions (character)}
+\format{
+An object of class \code{character} of length 5.
+
+An object of class \code{character} of length 4.
+}
+\usage{
+ordinal_link(values = values_ordinal_link)
+
+values_ordinal_link
+
+odds_link(values = values_odds_link)
+
+values_odds_link
+}
+\arguments{
+\item{values}{For \verb{*_link()}, a character string from among the possible
+values encoded in \verb{values_*_link}. See the examples below.}
+}
+\description{
+The ordinal and odds link functions of an ordinal regression model.
+}
+\details{
+These parameters are used by ordinal regression models specified by
+\code{parsnip::ordinal_reg()}, for example \code{parsnip::set_engine('polr')}. The
+nomenclature is taken from Wurm et al (2021), who characterize the pair of
+functions as a composite link function. Note that different engines support
+different subsets of link functions.
+}
+\examples{
+values_ordinal_link
+ordinal_link()
+values_odds_link
+odds_link()
+}
+\references{
+Wurm, Michael J., Rathouz, Paul J., & Hanlon, Bret M. (2021).
+Regularized Ordinal Regression and the ordinalNet R Package. \emph{Journal of
+Statistical Software}, 99(6), 1–42. 10.18637/jss.v099.i06
+}
+\keyword{datasets}
diff --git a/tests/testthat/test-params.R b/tests/testthat/test-params.R
index 7a94ace5..6fa0b825 100644
--- a/tests/testthat/test-params.R
+++ b/tests/testthat/test-params.R
@@ -199,4 +199,8 @@ test_that("param values", {
   expect_equal(cal_method_reg()$values, values_cal_reg)
   expect_equal(balance_probabilities(TRUE)$values, TRUE)
   expect_equal(average_before_softmax(TRUE)$values, TRUE)
+  expect_equal(ordinal_link(letters[1:3])$values, letters[1:3])
+  expect_equal(ordinal_link()$values, values_ordinal_link)
+  expect_equal(odds_link(letters[4:6])$values, letters[4:6])
+  expect_equal(odds_link()$values, values_odds_link)
 })