If the objective is to regain social interaction with the person in question, one possible means is to allow her time by herself before attempting to establish communications with her.
If you feel that her reasons for being angry at yourself are fair, it may be worth finding a resolution for the problem. This could be done by simply talking about the matter and making compensations between one another until you both feel happy with the situation.
Apologies given in person show much more sincerity than those given over the phone, via email, instant messaging, social networking websites, etc. They show that you are willing to take responsibility face to face and that you aren't afraid to accept the consequences of you own actions.
Simple romantic gestures are a good way of backing up given apologies and showing your sincere attempt at resolving the person's negative emotions about the situation. This could include simple, traditional methods such as taking her out for a dinner or to see a film, giving her flowers, etc.
If you feel that a quick fix between the two of you is necessary, whether you feel she's fair for being angry at you or not, one method of resolving the issue may be to take full responsibility for the occurring events, however this isn't the most honest and sincere method for resolving the dispute.
There are many methods for regaining social interactions with people after disagreements and arguments, however after resolving the issue both people should feel happy with the situation.