How do I make my dad accept that he can no longer have a credit card? He has a cash card.

Peter,
Your dad won’t accept it but he will eventually forget about it. Good job on having already taken care of canceling the credit card. Let me encourage you to not go backwards.
When he brings up the card try diverting him. No need to explain why he can’t have it. He can’t remember. Just go along with him. Less stress for both of you.
“ It’s in the mail.” Or
“ We’ll get that ordered.”
“ it should be there any day now”.
Or “Today is my treat, you can get lunch next time.”
Think about the last few times he brought it up and write down what he said and what you Could have said. Keep it near the phone and try it next time he brings the card up.
This will pass and it will be replaced by other issues. He sees you as his best resource to solve his problems or as “the fun police”. By reassuring him you are able to keep a more positive relationship. 

My husband accepted the dangers of identity theft as the reason he shouldn't carry one.