You can with a normal attack, not touch attacks
Vital Strike says:
Benefit: When you use the attack action, you can make one attack at your highest base attack bonus that deals additional damage. Roll the weapon's damage dice for the attack twice and add the results together before adding bonuses from Strength, weapon abilities (such as flaming), precision based damage, and other damage bonuses. These extra weapon damage dice are not multiplied on a critical hit, but are added to the total.
This means that Vital Strike can only affect weapon damage rolls.
You can deal normal damage while holding a touch spell if that is a regular attack and not a touch attack. You have the option to deliver a touch attack spell with a regular attack, as described under Holding the Charge:
Holding the Charge: If you don't discharge the spell in the round when you cast the spell, you can hold the charge indefinitely. You can continue to make touch attacks round after round. (...) If your unarmed attack or natural weapon attack normally doesn't provoke attacks of opportunity, neither does this attack. 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.
With that said, if the spell is a weapon attack, then you could use Vital Strike while making attacks with your spell, like using a Holy Ice Weapon, which creates a weapon made out out magic, or a Dimensional Blade, which turns a weapon into a magical object that can be used as a weapon.
Rays are specifically ruled to work as if you were making an attack with a ranged weapon.
Some effects are rays. You aim a ray as if using a ranged weapon, though typically you make a ranged touch attack rather than a normal ranged attack.
This is also enforced by this FAQ item:
Do rays count as weapons for the purpose of spells and effects that affect weapons?
Yes. (See also this FAQ item for a similar question about rays and weapon feats.)
For example, a bard’s inspire courage ability says it affects “weapon damage rolls,” which is worded that way so don’t try to add the bonus to a spell like fireball. However, rays are treated as weapons, whether they’re from spells, a monster ability, a class ability, or some other source, so the inspire courage bonus applies to ray attack rolls and ray damage rolls.
The same rule applies to weapon-like spells such as flame blade, mage’s sword, and spiritual weapon–effects that affect weapons work on these spells.
Another classic example is the Flame Blade druid spell, which creates a scimitar of flames. Since the spell specifically says it works like a scimitar, it also gains any benefits granted to weapons, as scimitars are weapons.