According to the Bible it is the closest relationship which is NOT incest. The Biblical definition of incest extends to aunts and uncles and to grandparents, but not to cousins. Of course the Bible forbids sex outside marriage.
As for the law, in most parts of the world it is legal to marry your first cousin and / or have sex with your first cousin. But in the USA law varies widely from state to state.
First cousin sex and marriage is generally frowned on in society. It's not advisable to have children with your first cousin because of the risk of inbreeding of recessive genetic defects.
You haven't actually specified a number of points:
- OK by whom? OK by God, OK by the law, or OK by society in general?
- Is your cousin of legal age, and are you?
- What is your gender, and what is your cousin's gender?
- Do you plan to use contraception?