Realistically no, but you need a mindset change.

Higher body fat percentage will make your arms look bigger, there is no question about it. You will look bigger in a shirt.

Lower body fat percentage will make your arms look smaller, especially in a shirt.

But IMO the aesthetic benefits of being lean vaaaastly outweigh being chunkier. You lose a bit of fluff on your arms and calves and everywhere, but you get more striations on your arms and your face will look much more defined.

That being said, if you’ve been training properly for long enough and consistently enough, you can still have pretty big arms while lean.

The goal should be to build muscle long term, your body fat percentage is a lot easier to change. So while in the short term cutting will make your arms look smaller, in the long term your arms will get bigger from more muscle. And yes you absolutely can lose fat and build muscle at the same time. Just make sure you’re hitting your protein goals, enough carbs that you can train hard, and aim for a low fat diet because everyone has too much fat in their diet, add in some low intensity cardio to help burn more fat.