Not as a full round action, but as a standard action you can vital strike a target while utilizing spell strike.
Note, you can not spell combat and vital strike in the same round, so you would have had to of cast the spell you're using spell strike with previously.
Notably, spellstrike is not an action, it's a rider that happens when you attack a target with a touch spell. Note that vital strike boosts the weapon damage, not the spell damage, so there are probably better feats to take with your magus.
Nope.
Spellstrike is a non-action, Vital Strike is a standard action.
So right off the bat, no, there's no possible way to combine those two things for a full round action.
To dig deeper:
Spellstrike is nothing more than a method to deliver touch spells. It will occur in one of two ways:
1. After anyone casts a touch spell, during the same turn they get a free action to deliver the touch spell. For a Magus, this delivery can be via a weapon attack due to Spellstrike. As a free action this explicitly contradicts Vital Strike, which requires the attack action.
2. After attempting the free touch, if you still have a charge of your touch spell (due to it being a multi-charge spell like Frostbite or you missing), any weapon attack will deliver the spell. At this point it can be delivered via Vital Strike.
So, to combine the two in the span of a single round, you would have to cast a touch spell without using your standard action (or be Mythic and have an extra standard action lying around, but we'll assume that's not the case). Then you use Vital Strike to deliver it. If that whiffs, you still get your free attempt at a touch, assuming we're still in the same round as casting it.
Basically? You just want Quicken Spell. Quickened Shocking Grasp -> whatever you want with your move action -> Vital Strike with a Spellstrike chaser.
But that's about the only way to do it. And it's still not a full round action.
+1
Worth noting vital strike will not increase your spell damage. It will only multiply the weapon damage dice.
Vital Strike takes a standard action which is already taken up by the casting of your spell.
But you could have a held charge.