diff --git a/Include/internal/pycore_bitutils.h b/Include/internal/pycore_bitutils.h
index 0bd3270fe82e5c..006bbef422cce5 100644
--- a/Include/internal/pycore_bitutils.h
+++ b/Include/internal/pycore_bitutils.h
@@ -17,9 +17,8 @@ extern "C" {
 #  error "this header requires Py_BUILD_CORE define"
 #endif
 
-#if defined(__clang__) || \
-    (defined(__GNUC__) && \
-     ((__GNUC__ >= 5) || (__GNUC__ == 4) && (__GNUC_MINOR__ >= 8)))
+#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. */
@@ -34,7 +33,8 @@ extern "C" {
 static inline uint16_t
 _Py_bswap16(uint16_t word)
 {
-#ifdef _PY_HAVE_BUILTIN_BSWAP
+    // bpo-41617: __builtin_bswap16() is not available in clang 3.0 and older.
+#if _Py_has_builtin(__builtin_bswap16) || defined(_PY_HAVE_BUILTIN_BSWAP)
     return __builtin_bswap16(word);
 #elif defined(_MSC_VER)
     Py_BUILD_ASSERT(sizeof(word) == sizeof(unsigned short));
@@ -49,7 +49,7 @@ _Py_bswap16(uint16_t word)
 static inline uint32_t
 _Py_bswap32(uint32_t word)
 {
-#ifdef _PY_HAVE_BUILTIN_BSWAP
+#if _Py_has_builtin(__builtin_bswap32) || defined(_PY_HAVE_BUILTIN_BSWAP)
     return __builtin_bswap32(word);
 #elif defined(_MSC_VER)
     Py_BUILD_ASSERT(sizeof(word) == sizeof(unsigned long));
@@ -66,7 +66,7 @@ _Py_bswap32(uint32_t word)
 static inline uint64_t
 _Py_bswap64(uint64_t word)
 {
-#ifdef _PY_HAVE_BUILTIN_BSWAP
+#if _Py_has_builtin(__builtin_bswap64) || defined(_PY_HAVE_BUILTIN_BSWAP)
     return __builtin_bswap64(word);
 #elif defined(_MSC_VER)
     return _byteswap_uint64(word);
diff --git a/Include/pymacro.h b/Include/pymacro.h
index 856cae774d61c7..4cd811070d7701 100644
--- a/Include/pymacro.h
+++ b/Include/pymacro.h
@@ -127,4 +127,19 @@
     Py_FatalError("Unreachable C code path reached")
 #endif
 
+
+// Test if the compiler has the specified builtin function.
+//
+// __has_builtin() is used if the compiler provides it.
+// Otherwise, always return 0.
+// For example, clang and GCC 10 provide __has_builtin().
+//
+// _Py_has_builtin() should not be used to detect support for a builtin macro;
+// use #ifdef instead.
+#ifdef __has_builtin
+#  define _Py_has_builtin(x) __has_builtin(x)
+#else
+#  define _Py_has_builtin(x) 0
+#endif
+
 #endif /* Py_PYMACRO_H */
diff --git a/Misc/NEWS.d/next/Build/2020-08-24-18-34-01.bpo-41617.sKKXz7.rst b/Misc/NEWS.d/next/Build/2020-08-24-18-34-01.bpo-41617.sKKXz7.rst
new file mode 100644
index 00000000000000..715eadbee896f1
--- /dev/null
+++ b/Misc/NEWS.d/next/Build/2020-08-24-18-34-01.bpo-41617.sKKXz7.rst
@@ -0,0 +1,2 @@
+Fix ``pycore_bitutils.h`` header file to support old clang versions:
+``__builtin_bswap16()`` is not available in LLVM clang 3.0.