Yes, provided they meet all the requirements an employee would meet. 

The amount of money they receive from Social Security does not count as income to allow them to contribute money to an IRA.

They can have either a Roth or a Traditional IRA.  The rules for contributions to either do not include Social Security income as eligible income.

Dusty Ernie

But after reading on the IRS website, it appears that they can contribute to a Solo 401k, up the amount of self employment earnings, with respect to also some special deductions to calculate the amount deductible?  Correct?

Also, thank you Dusty Ernie.

I will add my usual "What does your PAID tax professional say?"

"But after reading on the IRS website, it appears that they can contribute to a Solo 401k, up the amount of self employment earnings, with respect to also some special deductions to calculate the amount deductible?  Correct?" Yes, but .... 

What does your PAID pension plan advisor say? Maybe try something like https://www.fidelity.com/calculators-tools/ira-contribution-calculator  and https://individual.troweprice.com/public/Retail/Retirement/Small-Business-Retirement-Plans/Individua... 

You have not given nearly enough information to get a correct answer.