Perhaps you could stress to her that the fraternity is a lifetime membership, and that it would be to your benefit, as you could make professional networking contacts, etc.

If you and said girlfriend were to get married to each other, every little bit helps for networking, getting your career path on the right track, etc. Most women like to see their men succeed, and if you can show her that there are long-ranging professional benefits, as well as social ones, she might just change her mind.