Yes, you can file your tax return as self-employed. 

Just keep in mind! You don't need any proof of your income to file your tax return, but State or IRS can send a notice of intent to audit you.

The best way to prove your cash income is your accounting records. Any time when you receive the money you can deposit cash into your bank account. Bank deposit records are an excellent source of proof. 

Manual tracking system on your computer/software averse: Pick up a ledger or accounting pad with ruled columns at an office supply store and get into the habit of recording every bit of cash that comes your way in payment for services rendered. Record the date, reason for the payment and amount.

Software Program or Smartphone Application record can prove your cash income.