diff --git a/cpp/src/arrow/CMakeLists.txt b/cpp/src/arrow/CMakeLists.txt
index 42b0bcc151c..0cc4765a79c 100644
--- a/cpp/src/arrow/CMakeLists.txt
+++ b/cpp/src/arrow/CMakeLists.txt
@@ -739,7 +739,8 @@ set(ARROW_COMPUTE_SRCS
     compute/kernels/vector_selection.cc
     compute/kernels/vector_selection_filter_internal.cc
     compute/kernels/vector_selection_internal.cc
-    compute/kernels/vector_selection_take_internal.cc)
+    compute/kernels/vector_selection_take_internal.cc
+    compute/kernels/vector_swizzle.cc)
 
 if(ARROW_COMPUTE)
   # If libarrow_compute.a is only built, "pkg-config --cflags --libs
@@ -789,7 +790,6 @@ if(ARROW_COMPUTE)
        compute/kernels/vector_select_k.cc
        compute/kernels/vector_sort.cc
        compute/kernels/vector_statistics.cc
-       compute/kernels/vector_swizzle.cc
        compute/key_hash_internal.cc
        compute/key_map_internal.cc
        compute/light_array_internal.cc
diff --git a/cpp/src/arrow/compute/initialize.cc b/cpp/src/arrow/compute/initialize.cc
index d126ac951ff..d88835da04a 100644
--- a/cpp/src/arrow/compute/initialize.cc
+++ b/cpp/src/arrow/compute/initialize.cc
@@ -54,7 +54,6 @@ Status RegisterComputeKernels() {
   internal::RegisterVectorRunEndDecode(registry);
   internal::RegisterVectorPairwise(registry);
   internal::RegisterVectorStatistics(registry);
-  internal::RegisterVectorSwizzle(registry);
 
   // Aggregate functions
   internal::RegisterHashAggregateBasic(registry);
diff --git a/cpp/src/arrow/compute/registry.cc b/cpp/src/arrow/compute/registry.cc
index 37e9d6c930a..be0ebd32016 100644
--- a/cpp/src/arrow/compute/registry.cc
+++ b/cpp/src/arrow/compute/registry.cc
@@ -287,6 +287,7 @@ static std::unique_ptr<FunctionRegistry> CreateBuiltInRegistry() {
   RegisterDictionaryDecode(registry.get());
   RegisterVectorHash(registry.get());
   RegisterVectorSelection(registry.get());
+  RegisterVectorSwizzle(registry.get());
 
   RegisterScalarOptions(registry.get());
   RegisterVectorOptions(registry.get());