Hooking up a microphone to a guitar amplifier

Is it possible? If so how?

Well....

It depends on your mic and cable.

If you have a dynamic mic it could have a guitar-like plug at the end of the cable, in which case you could just plug it in. If it has an XLR plug you could look for an adapter, or you could get a new cable.

If you have a condenser mic you pretty much can't because you need the XLR cable to get the phantom power to the mic.

However, I wouldn't plug a mic into a guitar amp. Plug your guitar into your amp and then scream into the pickup. If you have the amp up loud enough you should be able to faintly hear your scream. The amp is made to deal with the output of guitar pickups, not microphones which are essentially voice pickups. I don't know all the technical stuff about impedance and such, but I've always heard it's not a good idea. If you're just messing around with low volumes it probably won't hurt anything, but I wouldn't consider it a performance solution.