Can one marry a cousin?

Yes. A cousin is not a mahram and Islam permits marriage between cousins.
The Qur'an mentions the lawfulness of the daughters of paternal and maternal uncles and aunts for the Prophet ﷺ, and he himself married Fatimah to Ali, his cousin. However, some advise genetic screening for families with a history of hereditary disease, as a precaution. Remember too that if the male cousin is the woman's wali, he may not marry her to himself; a wali hakim is needed. See Mahram.