No way! There is no age limit to applying for credit cards, loans, mortgages, or any other type of money lending scheme. It's true that part of having good credit is a solid history of on-time payments, but it's never too late to get started.
If you've made it this long in your life without credit, you might wonder why you need it at all. Assuming you live on the grid even a little bit, you've probably used a utility, rented a car or an apartment, or lived in a house that had a mortgage. If you were simply relying on someone else's credit to enjoy those things, it's time to step out on your own. Build that credit! You never know when you'll need it. People die, people get divorced; it sucks, but it's true.
WalletHub updates their lists frequently with cards available for people just getting into the credit game. Your best option will probably be a "secured" card — one that requires a small deposit and will have higher interest rate. Once you've established a solid payment history with a "secured" card, you can move on up to the real deal. Paying your balance in full each month will help you to establish a positive record and bring your FICO score up.
Your FICO score is the number that banks and lenders use to qualify you as a customer or borrower. It is comprised of your payment history, available credit, and and how long you've had accounts open.
The higher your FICO score, the lower interest rate you'll qualify for on loans, mortgages, and even insurance premiums.