term-git-mode

(defun term-git-mode--get-branch ()
    (let ((branches (vc-call-backend 'git 'branches)))
      (when branches (car branches))))

(define-minor-mode term-git-mode
  "show current branch in modeline in terminal-modes"
  :lighter (:eval (let ((git-branch (term-git-mode--get-branch)))
                    (if git-branch
                        (format " git:%s" git-branch)
                      ""))))
                      
 (add-hook 'term-mode-hook 'term-git-mode)