Question: My job is one that does not require that I pay Social Security taxes. Will I be eligible for Medicare when I turn 65?
Answer: It’s possible that you will be eligible for Medicare. Many city, state or federal employees, as well as some self-employed, do not pay Social Security taxes. However, there are 2 different taxes, a Social Security tax and a Medicare tax. Even if you aren't paying Social Security tax, you or your employer MAY still be paying Medicare tax. The only way to know is to look on your pay stub or W-2, it shows it in either of these places. It will say Medicare Tax.
Also, if you are married or were married for at least 10 years and your spouse paid Medicare taxes for at least 10 years, you may qualify under your spouse’s or ex-spouse’s Medicare tax payment.