Can i claim my cousin as a dependent if he has been living with me this year?

If the cousin passes all the tests to be a qualifying relative then you can claim them .....

Here are the complete rules for Claiming an Exemption for a Dependent:

- You cannot claim any dependents if you, or your spouse if filing jointly, could be claimed as a dependent by another taxpayer.
- You cannot claim a married person who files a joint return as a dependent unless that joint return is only a claim for refund and there would be no tax liability for either spouse on separate returns.
- You cannot claim a person as a dependent unless that person is a U.S. citizen, U.S. resident alien, U.S. national, or a resident of Canada or Mexico.
- You cannot claim a person as a dependent unless that person is your qualifying child or qualifying relative.

Requirements to be a Qualifying Relative:

1. The person cannot be your qualifying child or the qualifying child of any other taxpayer.
2. The person either (a) be related to your in one of the following ways:
Your child, stepchild, foster child, or a descendant of any of them
Your brother, sister, half brother, half sister, stepbrother, or stepsister.
Your father, mother, grandparent, or other direct ancestor, but not foster parent.
Your stepfather or stepmother.
A son or daughter of your brother or sister.
A brother or sister of your father or mother.
Your son-in-law, daughter-in-law, father-in-law, mother-in-law, brother-in-law, or sister-in-law.
or (b) must live with you all year as a member of your household (and your relationship must not violate local law).
3. The person's gross income for the year must be less than $4,000 (social security does not count).
4. You must provide more than half of the person's total support for the year.

There is a very good worksheet to help you determine how much support you provide. It is on page 15 of IRS Pub. 501
http://www.irs.gov/pub/irs-pdf/p501.pdf