I have a window AC unit rated at 115V 6.8 amps. If I wanted to plug the AC into a wall outlet, how do I determine if the wiring in the wall can safely handle the current. The wall outlet is a 3 prong US outlet and is 120V. However, if it can't be wired to the outlet, what would I need to run wiring 100ft to the connect it to the breaker?
A typical US wall receptacle is a 15A receptacle, and is connected to a 15 or 20A circuit breaker. So a little math shows it would use 45% or 33% of a the capacity of a circuit.
This size of load requires some caution. If when the AC cycles it causes brown-outs or trips a breaker you should find another place for the AC. But really you should be fine as long as you don't have a bunch of other high current stuff plugged into that circuit. If you want to be pro-active you could figure out which breaker feeds the receptacle you want to use, turn it off and look at the rated amps on the handle. Then identify the other receptacles connected to that circuit and add up typical amps of connected devices. If devices are listed in watts then calculate 115 watts per amp.
As a general rule if you ever trip a breaker you should identify every thing that stopped working when tripped and redistribute loads to prevent it from happening again, repeated tripping will weaken a breaker and exacerbate the problem.
If you experience tripping and can't redistribute loads (or you are just curious what it would take) 6.8A 100 feet away wouldn't cause excessive voltage loss caused by the wire size, so you would only need a 15A breaker, #14 wire, and a 15A receptacle. Typically you could use 14/2+g (often called Romex) for the wire, but your path for the wire might encounter damp, hazardous, susceptible to damage situations or you might have local ordinances that restrict wiring methods that might rule out NM cable. It would certainly be acceptable and I would recommend using a 20A breaker, #12 wire, and a 20A or 15A duplex receptacle. It would cost a little more but gives future options.
The minimum for any 115V outlet should be 15A. But you should be able check that by finding the circuit breaker for that circuit at the panel and checking its current rating.
The problem you'll possibly run into is if there are OTHER high-current devices on that same circuit. If both that and the AC run at the same time you may get a breaker trip.