A 32-bit id is so little data with so little redundancy to exploit that a true "compression algorithm" is likely not going to help much. On the other hand, simply using a higher numeric base where you use letters as well as digits to represent the number probably accomplishes exactly what you're after. For example, here's the largest possible 32-bit integer value in different bases:
Base 36 ZIK0ZJ
Base 36 is a logical stopping point because the letters A-Z and the digits 0-9 give you exactly 36 symbols, so going to even higher bases would require introducing something less obvious and possibly difficult to type.
A six-digit "number" should be short enough for anyone to easily type by hand. I'll assume you can work out the trivial algorithm to convert a number from one base to another on your own.