diff --git a/dvc/scm/git/backend/dulwich.py b/dvc/scm/git/backend/dulwich.py
index 865aa50a9..98eec2ab6 100644
--- a/dvc/scm/git/backend/dulwich.py
+++ b/dvc/scm/git/backend/dulwich.py
@@ -200,7 +200,12 @@ class DulwichBackend(BaseGitBackend):  # pylint:disable=abstract-method
         raise NotImplementedError
 
     def branch(self, branch: str):
-        raise NotImplementedError
+        from dulwich.porcelain import Error, branch_create
+
+        try:
+            branch_create(self.root_dir, branch)
+        except Error as exc:
+            raise SCMError(f"Failed to create branch '{branch}'") from exc
 
     def tag(self, tag: str):
         raise NotImplementedError
diff --git a/dvc/scm/git/backend/pygit2.py b/dvc/scm/git/backend/pygit2.py
index 7f26eb6d0..e8cb3a6e7 100644
--- a/dvc/scm/git/backend/pygit2.py
+++ b/dvc/scm/git/backend/pygit2.py
@@ -116,7 +116,13 @@ class Pygit2Backend(BaseGitBackend):  # pylint:disable=abstract-method
         raise NotImplementedError
 
     def branch(self, branch: str):
-        raise NotImplementedError
+        from pygit2 import GitError
+
+        try:
+            commit = self.repo[self.repo.head.target]
+            self.repo.create_branch(branch, commit)
+        except GitError as exc:
+            raise SCMError(f"Failed to create branch '{branch}'") from exc
 
     def tag(self, tag: str):
         raise NotImplementedError