There is no objection to get married to cousins according to the Quran 4:23 which specified certain categories of women/men who are prohibited to get married to. The Prophet got married to Umm Habibah bint Abu Sufyan who was the Prophet’s cousin.

 

However, a better question may be raised, namely, is it preferable for a Muslim to marry those who are outside one’s family? The answer on this question varies according to circumstances. It may be preferable to marry non-relatives in case one aspires to develop further social networks. It may also be preferable if his relatives suffer from a certain disease or he may be afraid in case of divorce to dissever relations with his kith and kin.