Hi there
I feel for you - this is a hard one, when all you want is for your child to be happy. I agree with those who have said to encourage her to take part in activities which are outside school - join groups, play a sport, whatever, so she has a chance to meet new people. Before she does, talk to her about ways she can engage other people in conversation, and how to encourage people to be friends with her without seeming needy.
A change of school may be an idea, if that's a possibility for you. I had a hard time myself at the age of 11 or 12 when I hit adolescence and I became very socially awkward and felt isolated. I was pretty miserable for a couple of years, then just before I was 13 my parents moved me to a new school where I knew no-one. I had a fresh start, made a whole load of new friends and went on to have a very happy next 5 years. It's worth thinking about if you can.
See if you can do anything to help her - she is probably a bit old for playdates, although to be honest I still fix up playdates for my 10 year old sometimes - they don't always have the organisation skills to do ti themselves! Do you know anyone with kids similar ages that you could invite over as a family and your child would have a chance to get to know their kids?
Talking to other moms you can trust about this may help. My daughter had a bit of a rough patch with a couple of her friends, and as I felt able to talk to their mothers we were able to help the kids sort it out and spend quality time together, without letting them know we knew all about it!
I hope it works out for you both