Is it an accepted practice to notify the tower of a radio failure by cell phone, and use the cell phone as a radio, or are there other ways of dealing with radio failure?
Now, if the pilot has an emergency, they can exercise the emergency authority of the PIC as allowed in 14 CFR 91.3(b) to go ahead and use the cell phone. If it is just the radio failure though, that isn't usually an emergency since there are other procedures in place for radio failures.
Radio Failure Procedures
AIM 6-4-1 contains the procedures to use in the event of a radio failure.
Basically, if the pilot is in visual conditions (VMC) and can remain that way, they should fly VFR (visually) and land as soon as practical. If they can't remain in VMC then there are a number of rules which spell out the route and altitude that they should fly, as well as when they should start an instrument approach.
Once they get to an airport they will still need to get clearance to land if it is a towered airport.
AIM 4-3-13 covers that, and basically the tower will communicate with the pilot via light gun signals: