Since I've been on a cutting diet, I've been losing size in my arms. When I start back on a regular diet and workout , will my arms and oher muscles comeback because of memory?

The thing is, some of the size you've lost on your arms is fat, and if you are still hitting the gym and lifting weights, probably not that much is muscle. But yes, as soon as you eat at maintenance and lifting heavy, your muscles will remember what you do.

However, it's easier to lose fat than to build muscle (unless you are very lucky genetically) so keep lifting while you are cutting to reduce muscle loss.