The short answer is yes and it depends.
First, let's clarify who we're talking about here. If you are earning money as a side hustle, independent contractor, 1099, sole proprietor, or schedule C filers which are really all the same thing, you may be eligible based on these types of income to contribute to a solo 401(k). I find that some independent contractors don't realize they are independent contractors because they don't realize that a side hustle or 1099 income and ultimately a schedule C filer are one and the same.
The second point and why it depends if you can have a solo 401(k) is because you'll need to have earned income. The amount that you can contribute is found on your Schedule C line 31, net profit. The amount on line 31 is then reduced by 1/2 of self employment and multiplied by a maximum of 20% as a schedule C filer.
The maximum amount that you can contribute as an employer using this calculation is $58,000 if you're under 50 years old and an additional $6,500 for 50 or older. You can also make an employee contribution of up to $19,500 as long as you have the earned income. The amount you may contribute to your solo 401(k) could be reduced by any amounts you contribute to another retirement plan such as a workplace 401(k) plan.
The solo 401(k), depending on your plan documents, may allow you to make contributions including nondeductible contributions up to $58,000 for 2021. The benefit here is your ability to convert the nondeductible contributions to the Roth solo 401(k). The contributions are not deductible like your traditional solo 401(k) contributions but the benefit is realized when you convert these dollars to the Roth side of your solo 401(k) or Roth IRA. This type of money movement is known as the Mega Backdoor Roth strategy. Most brokerage firms do not allow for this type of transaction but you can find custom plan documents that can expand a new or existing solo 401(k) to include the Mega Backdoor Roth strategy.
If you want a simplified version of the solo 401(k) you can open and fund a prototype plan at most brokerage firms that offer solo 401(k) accounts. The difference is the documents and certain transactions such as the Mega Backdoor Roth strategy mentioned earlier. It's a great first step in saving for your retirement as an independent contractor and offers almost exactly the same types of investments.