Can I marry my maternal cousin?

Both Hindu Marriage and Special Marriage acts prohibit marriages between first cousins, unless the custom of the community permits it. If you are able to prove to the satisfaction of the court that such a usage (marriage between first cousins) is common practice and has been consistently carried out through a long period, and the court grants permission, you can.

That marriages between blood relations might lead to health issues for the child has been suspected for several years. Now, a detailed analysis of the issue involving over 11,000 children, born out of consanguineous marriages, revealed congenital anomalies in 386 of them. This figure of 3 per cent contrasts with the 1.6 per cent in children born of out of non-blood-relations unions. 

If there is a proven custom that has attained legal sanction then such marriage is possible.

However the social stigma that is attached to such marriages and/or incidences of health issues is to be looked into by you.