diff --git a/src/pip/_internal/utils/misc.py b/src/pip/_internal/utils/misc.py
index c1faee3947d..fdd7de908a9 100644
--- a/src/pip/_internal/utils/misc.py
+++ b/src/pip/_internal/utils/misc.py
@@ -653,6 +653,7 @@ def call_subprocess(
     show_stdout=True,  # type: bool
     cwd=None,  # type: Optional[str]
     on_returncode='raise',  # type: str
+    returncodes=None,  # type: Optional[Iterable[int]]
     command_desc=None,  # type: Optional[str]
     extra_environ=None,  # type: Optional[Mapping[str, Any]]
     unset_environ=None,  # type: Optional[Iterable[str]]
@@ -661,9 +662,13 @@ def call_subprocess(
     # type: (...) -> Optional[Text]
     """
     Args:
+      returncodes: an iterable of integer return codes that are acceptable,
+        in addition to 0. Defaults to None, which means [].
       unset_environ: an iterable of environment variable names to unset
         prior to calling subprocess.Popen().
     """
+    if returncodes is None:
+        returncodes = []
     if unset_environ is None:
         unset_environ = []
     # This function's handling of subprocess output is confusing and I
@@ -740,7 +745,7 @@ def call_subprocess(
             spinner.finish("error")
         else:
             spinner.finish("done")
-    if proc.returncode:
+    if proc.returncode and proc.returncode not in returncodes:
         if on_returncode == 'raise':
             if (logger.getEffectiveLevel() > std_logging.DEBUG and
                     not show_stdout):
diff --git a/src/pip/_internal/vcs/__init__.py b/src/pip/_internal/vcs/__init__.py
index 7fc53526123..a432c3868e8 100644
--- a/src/pip/_internal/vcs/__init__.py
+++ b/src/pip/_internal/vcs/__init__.py
@@ -17,7 +17,7 @@
 
 if MYPY_CHECK_RUNNING:
     from typing import (  # noqa: F401
-        Dict, Optional, Tuple, List, Type, Any, Mapping, Text
+        Any, Dict, Iterable, List, Mapping, Optional, Text, Tuple, Type
     )
     from pip._internal.utils.ui import SpinnerInterface  # noqa: F401
 
@@ -467,6 +467,7 @@ def run_command(
         show_stdout=True,  # type: bool
         cwd=None,  # type: Optional[str]
         on_returncode='raise',  # type: str
+        returncodes=None,  # type: Optional[Iterable[int]]
         command_desc=None,  # type: Optional[str]
         extra_environ=None,  # type: Optional[Mapping[str, Any]]
         spinner=None  # type: Optional[SpinnerInterface]
@@ -480,8 +481,10 @@ def run_command(
         cmd = [self.name] + cmd
         try:
             return call_subprocess(cmd, show_stdout, cwd,
-                                   on_returncode,
-                                   command_desc, extra_environ,
+                                   on_returncode=on_returncode,
+                                   returncodes=returncodes,
+                                   command_desc=command_desc,
+                                   extra_environ=extra_environ,
                                    unset_environ=self.unset_environ,
                                    spinner=spinner)
         except OSError as e:
diff --git a/src/pip/_internal/vcs/git.py b/src/pip/_internal/vcs/git.py
index dc80a0532ef..e32bba8c1c4 100644
--- a/src/pip/_internal/vcs/git.py
+++ b/src/pip/_internal/vcs/git.py
@@ -84,14 +84,18 @@ def get_current_branch(self, location):
         Return the current branch, or None if HEAD isn't at a branch
         (e.g. detached HEAD).
         """
-        args = ['rev-parse', '--abbrev-ref', 'HEAD']
-        output = self.run_command(args, show_stdout=False, cwd=location)
-        branch = output.strip()
+        # The -q causes the command to exit with status code 1 instead of
+        # 128 if "HEAD" is not a symbolic ref but a detached HEAD.
+        args = ['symbolic-ref', '-q', 'HEAD']
+        output = self.run_command(
+            args, returncodes=(1, ), show_stdout=False, cwd=location,
+        )
+        ref = output.strip()
 
-        if branch == 'HEAD':
-            return None
+        if ref.startswith('refs/heads/'):
+            return ref[len('refs/heads/'):]
 
-        return branch
+        return None
 
     def export(self, location):
         """Export the Git repository at the url to the destination location"""