I am divorced and have two kids and want to know if I am allowed to claim one of them on my income tax

Only the custodial parent can claim the child. It does not count who is paying child support. The custodial parent is the parent with whom the child lived for the longer period based on nights spent.
The other parent is the non-custodial parent. Also, non-custodial parent can claim the child only if the custodial parent signs a release Form 8332 or there is a court order meeting the IRS requirements. Your U.S. Tax Return: Child of separated or divorced parents (http://taxipay.blogspot.com/2008/03/child-of-separated-or-divorced-parents.html)

Jason:

Who gets to claim which child is almost ALWAYS an issue with divorced parents, so much so that the issue is often addressed in the divorce decree, which is a LEGAL document that the IRS will abide by.

You should contact your ex-spouse and discuss it with her. It may make more sense for her to claim both of the children if she makes more money than you, or if she qualifies for the Earned Income Credit. This should be a simple negotiation, with give-and-take and possibly offering to share the enhanced refund. Try NOT to get emotional about it and treat it as a business deal.

As ATE said, this should be spelled out in your divorce decree. If its not addreessed specifically, then the custodial parent is the one with the right to claim them as Mukat said.