You can deliver a touch spell with a monk's unarmed strike, but there's not much benefit: you can't make the unarmed attack in the same round that you cast the spell.
Normally, when you cast a touch spell you can either touch an opponent for free, or hold the charge:
Touch Spells in Combat
Many spells have a range of touch. To use these spells, you cast the spell and then touch the subject, either in the same round or any time later. In the same round that you cast the spell, you may also touch (or attempt to touch) the target. You may take your move before casting the spell, after touching the target, or between casting the spell and touching the target.
However, you only get a free touch as part of the spell, not a free attack. Since an unarmed strike is an attack action, you would have to cast the spell one round, then make an unarmed strike in the following round.
While you can deliver a touch spell with an unarmed strike or natural weapon, there's no benefit since it takes two rounds anyway. It's actually harder, because to deliver a touch attack with an unarmed strike requires you to hit their full AC, not just touch AC:
If the attack hits, you deal normal damage for your unarmed attack or natural weapon and the spell discharges. If the attack misses, you are still holding the charge.
However, this still has its uses:
- Since you can hold a charge indefinitely until you touch something, the monk can cast the spell ahead of time and hold it until a combat encounter
- Some spells like chill touch allow multiple hits from one casting
- Sometimes you want to deal a lot of damage in one round so the enemy can't escape or flee
- You might have feats or items that grant some bonus to unarmed attacks but not touch attacks
- Some creatures have always-on touch attacks that don't need to be cast, such as a lich's paralyzing touch
Source: D20 SRD, Actions in Combat.