To my knowledge, having served in the armed forces and been in combat:
Technically speaking, no. It doesn't matter how high-ranking a military official is, he does not have the authority to "deputize" a private citizen into the military. Be it against the person's will (which would be deemed unconstitutional) or if the person's all for it (there is still the swearing in, the qualification/ASVAB testing processes, the MEP tests, etc.), the only person who may be called into duty who is NOT already a soldier is a retired/ETS'ed soldier, and even then it's only allowable up to a certain age, and depending on how long they've been on inactive duty.
For example:
In the Army, which I was in, you are automatically enlisted for eight years. You will spend x amount of years on active duty. After those three years I ETS'ed (out-processed) and spent the remaining five years of my enlistment on inactive duty, which means I came home and went about life as usual as a civilian.
During those five years, however, I could have been called back in at any time. I'd have been given the military equivalent of "refreshment" training and rotated back into active duty until I was no longer needed, at which case I would have out-processed again and returned to inactive "civilian" life for the remainder of my inactive duty time. After that period of inactive duty was up, I still could have been (but was less likely to have been) called back into duty, unless I was 35 years old or older (Army enlistment's cut-off age for a new recruit). I'm pushing 34 right now and haven't been called back in, so I don't see it happening for me any time soon.
Now...if your script operates on a realistic basis, forget about a General recruiting a civilian directly into combat. It does not, and never will, work like that. However...I don't see a problem if you decided that your civilian character, of his own accord, volunteered to assist. But even then, he's still a private citizen and does not have the freedoms of combat (how's that for an oxymoron) that an enlisted soldier would. Forget what you've seen in the movies. He would not be made privy to any confidential information (the military's confidentiality clauses have three tiers; "confidential", "secret" and "top secret") and he would not be considered part of any team, squad, platoon, company, unit or division. He'd basically be the equivalent of a regular guy the police give permission to go on a ride-along.
But if you want to get absolutely downright technical, during a siege civilians are treated as POW's; which means, in conjunction with the Geneva Convention, the military's primary concern would be the safety and sequestering of private citizens and the minimalization of risk to their persons. Recruiting them on the spot and handing them over a weapon is an antithesis to this.