diff --git a/src/requests/auth.py b/src/requests/auth.py
index 4a7ce6dc14..dbe6e13a97 100644
--- a/src/requests/auth.py
+++ b/src/requests/auth.py
@@ -183,9 +183,13 @@ def sha512_utf8(x):
         p_parsed = urlparse(url)
         #: path is request-uri defined in RFC 2616 which should not be empty
         path = p_parsed.path or "/"
+
+        # Normalize path by removing excess leading slashes (same as adapters.py)
+        if path.startswith("//"):
+            path = f"/{path.lstrip('/')}"
+
         if p_parsed.query:
             path += f"?{p_parsed.query}"
-
         A1 = f"{self.username}:{realm}:{self.password}"
         A2 = f"{method}:{path}"
 
diff --git a/tests/test_requests.py b/tests/test_requests.py
index 75d2deff2e..5d021da880 100644
--- a/tests/test_requests.py
+++ b/tests/test_requests.py
@@ -805,6 +805,30 @@ def test_DIGESTAUTH_QUOTES_QOP_VALUE(self, httpbin):
             r = requests.get(url, auth=auth)
             assert '"auth"' in r.request.headers["Authorization"]
 
+    def test_DIGEST_AUTH_NORMALIZES_DOUBLE_SLASH_PATH(self):
+        """Digest auth URI should normalize double slashes to match request path.
+        
+        Regression test for GitHub issue #6784.
+        """
+        auth = HTTPDigestAuth("user", "pass")
+        auth.init_per_thread_state()
+        
+        # Simulate server challenge
+        auth._thread_local.chal = {
+            "realm": "test",
+            "nonce": "abc123",
+            "qop": "auth",
+            "algorithm": "MD5"
+        }
+        
+        # URL with double slash in path
+        url = "http://example.com//path/to/resource"
+        header = auth.build_digest_header("GET", url)
+        
+        # The URI should be normalized to single slash
+        assert 'uri="/path/to/resource"' in header
+        assert 'uri="//path/to/resource"' not in header
+
     def test_POSTBIN_GET_POST_FILES(self, httpbin):
         url = httpbin("post")
         requests.post(url).raise_for_status()