Yes. A certificate of deposit held at an FDIC-member bank is covered by federal deposit insurance up to $250,000 per depositor, per insured bank, per ownership category. That protection applies to your principal plus any accrued interest, and it means your money is safe even if the bank fails.
The limit is per ownership category, so deposits you hold individually, jointly, and in retirement accounts are insured separately, which can raise your total coverage at one bank. If you hold more than $250,000, you can stay fully covered by spreading deposits across categories or across multiple insured banks. CDs from credit unions carry equivalent coverage through the NCUA.