diff --git a/src/pip/_internal/network/session.py b/src/pip/_internal/network/session.py
index 4af800f12fe..2e1d539d1a0 100644
--- a/src/pip/_internal/network/session.py
+++ b/src/pip/_internal/network/session.py
@@ -19,6 +19,8 @@
 import mimetypes
 import os
 import platform
+import shutil
+import subprocess
 import sys
 import urllib.parse
 import warnings
@@ -163,6 +165,18 @@ def user_agent():
     if setuptools_dist is not None:
         data["setuptools_version"] = str(setuptools_dist.version)
 
+    if shutil.which("rustc") is not None:
+        # If for any reason `rustc --version` fails, silently ignore it
+        try:
+            rustc_output = subprocess.check_output(["rustc", "--version"])
+        except Exception:
+            pass
+        else:
+            # The format of `rustc --version` is:
+            # `b'rustc 1.52.1 (9bc8c42bb 2021-05-09)\n'`
+            # We extract just the middle (1.52.1) part
+            data["rustc_version"] = rustc_output.split(b" ")[1].decode()
+
     # Use None rather than False so as not to give the impression that
     # pip knows it is not being run under CI.  Rather, it is a null or
     # inconclusive result.  Also, we include some value rather than no