Can a retired individual do a back door roth conversion from an ira. I am retired (age 66) with no income beyond Social Security and two partial pensions.

No.  A backdoor Roth is used by people whose income it too high to permit a direct Roth contribution so they make a non-deductible Traditional IRA contribution and then convert that to a Roth.

To make *any* IRA contribution you must have taxable compensation (money that your worked for) or spouse worked for on a joint return, at least as much as the contribution.

If your only income is SS and retirement income, you are not eligible to make any IRA contribution at all.

If you instead want to do a Roth conversion from an already existing balance in a traditional IRA, there are no restrictions against doing so.