Yes, you can continue to contribute to an IRA even if you start collecting Social Security benefits. An IRA (and its corollary, the Roth IRA) is a tax-advantaged form of retirement account that allows you to save money during your working years so that you can withdraw it during retirement. There's no age limit for contributing to an IRA, meaning you can do so at any time in your life. However, you can only contribute earned income to this account, not investment income.
So, even if you're technically retired, you must work in some way to make additional contributions to the IRA. A financial advisor may be able to help you determine how to manage your IRA. SmartAsset's free advisor search tool can help you find advisors who serve your area. Yes, you can contribute to an IRA after you retire (with caveats).
Contributing to an IRA or Roth IRA during retirement has benefits, depending on your particular situation. First, make sure that you actually have the taxable compensation required to make the traditional IRA or Roth IRA contributions you're considering making. If you don't have taxable compensation but file a joint return with an earning spouse, you can open an IRA in your name and make contributions through a spousal IRA. After confirming that you are eligible to make contributions to an IRA during retirement, you may need guidance on how much you can contribute or help evaluating whether a Roth or a traditional IRA is better for you.
If you are retired and your spouse has earned income, he or she can contribute to their own IRA and also make what is called a spousal contribution to your IRA. For contributions to a Roth IRA, make sure you can contribute to a Roth IRA right from the start. Since people usually contribute to IRAs throughout their lives and invest at the same time, IRA balances can be quite high when they reach retirement age.