I have a Hexblade Warlock Rogue, I have the cantrip Booming Blade and the Spell Wrathful Smite. As far as I understand RAW as Wrathful Smite is a Bonus action and Booming Blade is a Cantrip my character should (in theory) be able to attack with Booming Blade, and if it hits I can then use Wrathful Smite as well. Correct?
Yes, You Can!
Booming Blade is a cantrip with a one action casting time and Wrathful Smite is a Bonus Action Spell.
PHB, 202 States:
You can’t cast another spell during the same turn, except for a cantrip with a casting time of 1 action.
This fulfill that requirement - the Cantrip Action and the Bonus Action Spell slot.
Concentrate until you hit
It's also good to note that Wrathful Smite is a concentration spell and you can maintain that concentration until you actually hit the target. You can also cast the Wrathful Smite before Booming Blade so that when you hit, it's ready to go.
But should you?
This one is more up to you and the given situation, but it's something to consider. You get another d6 of damage (psychic), but the frightened condition only prevents the target from moving towards you. The booming blade doesn't trigger without movement and now the target has no reason to chase you (and in fact, can't.) There definitely are times and places, but in general divine smites are a better use of your spell slots unless you can make the frightened rider (or other spell smite rider) work for you beyond just damage.