diff --git a/Include/internal/pycore_byteswap.h b/Include/internal/pycore_byteswap.h
index 975e150dd91..2b20fc6c7d3 100644
--- a/Include/internal/pycore_byteswap.h
+++ b/Include/internal/pycore_byteswap.h
@@ -15,12 +15,9 @@ extern "C" {
 #  error "this header requires Py_BUILD_CORE define"
 #endif
 
-#if ((defined(__GNUC__) \
-      && ((__GNUC__ >= 5) || (__GNUC__ == 4) && (__GNUC_MINOR__ >= 8))) \
-     || (defined(__clang__) \
-         && (__clang_major__ >= 4 \
-             || (__clang_major__ == 3 && __clang_minor__ >= 2))))
-   /* __builtin_bswap16() is available since GCC 4.8 and clang 3.2,
+#if defined(__GNUC__) \
+      && ((__GNUC__ >= 5) || (__GNUC__ == 4) && (__GNUC_MINOR__ >= 8))
+   /* __builtin_bswap16() is available since GCC 4.8,
       __builtin_bswap32() is available since GCC 4.3,
       __builtin_bswap64() is available since GCC 4.3. */
 #  define _PY_HAVE_BUILTIN_BSWAP
@@ -34,7 +31,7 @@ extern "C" {
 static inline uint16_t
 _Py_bswap16(uint16_t word)
 {
-#ifdef _PY_HAVE_BUILTIN_BSWAP
+#if defined(_PY_HAVE_BUILTIN_BSWAP) || _Py__has_builtin(__builtin_bswap16)
     return __builtin_bswap16(word);
 #elif defined(_MSC_VER)
     Py_BUILD_ASSERT(sizeof(word) == sizeof(unsigned short));
@@ -49,7 +46,7 @@ _Py_bswap16(uint16_t word)
 static inline uint32_t
 _Py_bswap32(uint32_t word)
 {
-#ifdef _PY_HAVE_BUILTIN_BSWAP
+#if defined(_PY_HAVE_BUILTIN_BSWAP) || _Py__has_builtin(__builtin_bswap32)
     return __builtin_bswap32(word);
 #elif defined(_MSC_VER)
     Py_BUILD_ASSERT(sizeof(word) == sizeof(unsigned long));
@@ -66,7 +63,7 @@ _Py_bswap32(uint32_t word)
 static inline uint64_t
 _Py_bswap64(uint64_t word)
 {
-#ifdef _PY_HAVE_BUILTIN_BSWAP
+#if defined(_PY_HAVE_BUILTIN_BSWAP) || _Py__has_builtin(__builtin_bswap64)
     return __builtin_bswap64(word);
 #elif defined(_MSC_VER)
     return _byteswap_uint64(word);
diff --git a/Include/pyport.h b/Include/pyport.h
index 6505af46768..4bd4eb4751b 100644
--- a/Include/pyport.h
+++ b/Include/pyport.h
@@ -863,4 +863,16 @@ extern _invalid_parameter_handler _Py_silent_invalid_parameter_handler;
 #  define _Py_NO_RETURN
 #endif
 
+
+// Preprocessor check for a builtin preprocessor function. Always return 0
+// if __has_builtin() macro is not defined.
+//
+// __has_builtin() is available on clang and GCC 10.
+#ifdef __has_builtin
+#  define _Py__has_builtin(x) __has_builtin(x)
+#else
+#  define _Py__has_builtin(x) 0
+#endif
+
+
 #endif /* Py_PYPORT_H */
diff --git a/Misc/NEWS.d/next/Build/2020-11-13-15-04-53.bpo-41617.98_oaE.rst b/Misc/NEWS.d/next/Build/2020-11-13-15-04-53.bpo-41617.98_oaE.rst
new file mode 100644
index 00000000000..a5f35b25e8b
--- /dev/null
+++ b/Misc/NEWS.d/next/Build/2020-11-13-15-04-53.bpo-41617.98_oaE.rst
@@ -0,0 +1,3 @@
+Fix building ``pycore_bitutils.h`` internal header on old clang version
+without ``__builtin_bswap16()`` (ex: Xcode 4.6.3 on Mac OS X 10.7). Patch by
+Joshua Root and Victor Stinner.