when two computer communicating(sending and receiving) with each other through the twisted cable, then the current in the wire is ac or dc?
It may depend on the sort of signalling you are using, and on your definition of AC.

For true RS-232 serial communications, a "1" bit is represented by a negative voltage, and a "0" is represented by a positive voltage, so you might call that AC - but it is a series of pulses, and stays negative when the line is idle (no characters being transmitted). 

For many other serial protocols, the signal does not change polarity, but is still a series of pulses.  Whether you consider this AC with a DC offset or pulsing DC is up to you.