If this is your primary concern, unless you have some cash to burn, you might want to get deeper into things. Is the system original (1982)? If yes, then, it has probably given all it can. Otherwise, is the system air cooled or water cooled? In either case, loss of performance may very well be due to fouling of the condenser heat exchanger. In that case either clean the coils (for air cooled) or check and address the water circulation and temperatures (for water cooled).
In the worst (but totally survivable) case that your system can provide no further use: you should replace the entire refrigeration system (cold coil, compressor, condenser), but not the refrigeration compartment itself (the "ice box"). For that, see the links provided by others above. But in no case should you seriously consider replacing only the compressor in a typical refrigeration system as you describe. It can be done, but it is unlikely to work well for long. That is because of issues with contamination in the refrigeration circuit, and compatibility issues with refrigerants and lubricants which circulate within the system.
These systems are typically sized based on cubic feet of icebox volume. That's more to assure fast recovery after opening the lid than it is to maintaining temperature. There are other vendors with suitable systems, but many here have been well served with
Isotherm systems.