Error is usually used for uncontrolled contents such as user input, panic is usually used for static content.
Usually this regexp pattern is part of the code, so panic is not that unexpected, what do you think?

if it returns the error what would you do with the error?

In this context, I'd expect it to raise an error and halt the execution of program.

You can always check the pattern before you pass it to the code.

_, err := regexp.Compile(reg)
if err != nil {
  ...
}

router.Add(reg, ...)