Path of Raging Arcana

You can use wizard spells when not raging. 

Magic Awareness

3rd-level Path of Raging Arcana feature

As an action, you can open your awareness to the presence of concentrated magic. Until the end of your next turn, you know the location of any spell or magic item within 60 feet of you that isn’t behind total cover. When you sense a spell, you learn which school of magic it belongs to.

You can use this feature a number of times equal to your proficiency bonus, and you regain all expended uses when you finish a long rest.

Raging Magic

8th level Path of Raging Arcana class feature. 

You can cast spells though quite difficult. Each spell level has a limited casting ability based on your proficiency bonus. Each time you cast a spell your other spells of that level lose a cast use. 

Magic Burst

10th level Path of Raging Arcana feature 

You burst out magic within you using a casting usage. Higher the level the more damage. Dealing 2d6+ CON force damage. The attack will ignore your resistance and immunity. You don't make a save and you get knocked prone after usage. Can't be used during rage.  

Every level above 1st deals an extra 1d8 damage. 

Arcanic Rage

15th-level Path of Raging Arcana feature.

By using a spell your weapon attacks while raging are magic. When you cast the spell to activate it you don't get the benefits of casting it. You can't cast spells while raging.