Is she actively being bullied and excluded (Miss, we don't want her on our table) or is it just that noone wants to be her friend?
I have had experience of both and they can both be very hard to bear. With hindsight, I would say that while there was absolutely no excuse for the former and I totally blame my bullies (and the school!) for that, at the same time I can see where the latter was coming from; people do have a right to choose their friends and I was not brilliant at adapting to other people. I simply thought the things I enjoyed and was good at were better and more important than the things they wanted to talk about. I was not prepared to make an effort for other children, though looking back I realised I expected them to make quite an effort for me.
My dd who is probably brighter than me has had no problems of either kind. I think it is a combination of a number of factors:
a) her classmates are simply nicer people!
b) the schools clamp down very firmly on any bullying (though they obviously can't force people to be friends)
c) dd herself is very good at understanding other people and adapting to them
d) you wouldn't feel, when in dd's company, that she thinks the things she is good at are more valuable than the things somebody else is good at - I think children who talked to me did feel that. It was partly because my whole family thought that way, so it didn't occur to me that you could think differently.
I don't agree that children get bullied exclusively due to poor social skills: school playgrounds tend to have a culture and that can vary from school to school, or even from year group to year group. There are still places where you can get bullied from day one for having ginger hair or having a strange accent before you've had a chance to demonstrate social skills - and there are other schools with a totally different atmosphere. But obviously, even in schools with virtually no bullying, some people will be better liked than others and have more friends.
I think the advice to join clubs is a good one. If your dd finds she can get on with other children, it will boost her social confidence and that in itself can be a great help in getting on with other people.