Check your computer's manual for instructions on accessing the BIOS
settings. You'll be looking for the "Wake on......" section. Most
computers support a Wake on alarm feature.
The only thing I can think of (assuming you have a newer power-supply
and not an older one, in which case a timer on the power plug would
obviously do it) would be Not to turn off your machine but to let it go
to "sleep". I believe some utilities might then be able to wake it up
but I do not know personally any.