Yes. For this you must complete the New York State Voter Registration Form on the New York State Board of Elections website and mail it to your County Board of Elections.
And what should I do if I have waited almost 2 months for a response and haven't gotten anything?
In that case you should contact them at the phone number or address provided on the New York State Board of Elections website.
One final question: how do I know what my voter registration status is?