I get this question very often. The answer is yes you can. Medicaid is for low income individuals and is a benefit of your state. Medicare is a federal heath insurance for all Americans 65 and older or those on Social Security receiving disability benefits.
If you are on both Medicare and Medicaid, Medicare is your primary coverage. Medicaid pick up the difference. Also, you will have a Part D prescription plan. The Part D will be primary and the Medicaid will pick up most of the copays.
To get on Medicaid you will need to go to your local Social Services or welfare office.
Also of note, many of the Medicare Advantage insurance have special plans for those with both Medicare and Medicaid. These plans pay many extra benefits like OTC (over the counter) cards that can help with many OTC items not covered by insurance. Some of the plans have full dental and vision coverage and transportation services.