I never done this but I'm just giving some advices.

1. Talk to her about her gaming history. Ask her did she played some games when she was young or is she playing online  games currently.

2. Tell her that if you play games together you will be able to spend more time together. Don't try to force her, take a look does she really like it.

3. Try to rent some games ( if you don't have any ) from your friend that are really simple and don't requier fast reaction like in some FPS games or Guitar Hero. Play a few different games with her like Sims and Lego Star Wars, or Resident Evil and Grand Theft Auto and ask her what type does she likes. If she doesn't seem to like those games then try tekken and soul calibur, maybe she likes fighting games. Don't play games that include strippers or sex, she will hate it!

4.  While playing a game in 2 players focus on spending time with her instead of trying to win. Let her win when playing to prove her that it's not hard and it's fun. Don't get mad if she can't pass some levels even when she is trying to pass a level for 40 minutes and she is still loosing, help her out.

5. If you are going with her to town and see a game store close to you, ask her does any of those games catches her eye.