Path of the Rage Mage

Some barbarians are overcome by a fury powered not entirely
by their own will, crackling with arcane power. Known as
Rage Mages, these barbarians can cast a limited number of
spells even while raging, and slowly develop the ability to
have magic bleeding out of them into their melee attacks.
In Khorvaire, Rage Mages are most often found among
Mournborn warped by the Day of Mourning, creatures
touched by Kythri, and bearers of aberrant dragonmarks. The
reality storms that wrack Sarlona might also produce Rage
Mages, and sailors of the Thunder Sea claim they've seen
sahuagin who've demonstrated similar abilities. Few others
have the necessary connection to the raw eldritch power
needed to follow this path.

From "Archetypes of Eberron" by Will Brolley, Imogen Gingell, Laura Hirsbrunner (DMsGuild)

Destructive Potential

Starting at 3rd level, you can shape your raw arcane power
into defined effects. You learn an additional spell when you
reach certain levels in this class, as shown in the Rage Mage
Spells table. The spell counts as a Rage Mage spell for you,
but it doesn't count against the number of Rage Mage spells
you know.

Spell Rage

Beginning at 3rd level, scars from the raw arcane energies
suffusing you mark your skin with potent symbols of power,
subtly changing and empowering your rage. When you rage
while not wearing armor, you gain all of the benefits normally
granted by rage, along with the following benefits:
• You can cast Rage Mage spells while you are raging.
• Casting a spell that deals damage, requires an attack roll, or
causes a creature to make a saving throw counts as attacking
a hostile creature for the purpose of keeping your rage
active.

Fueled by Magic

Beginning at 6th level, your spell-enhanced rage bleeds over
to your melee weapons. While you are raging, your melee
weapon attacks are considered magical for the purpose of
overcoming immunity and resistance to nonmagical attacks
and damage.

Caustic Arcana

Starting at 10th level, your attacks embroil their targets in a
raging wisp of pure magic. If you hit a creature with a melee
weapon attack while raging, you can use a bonus action on
that turn to assail it with raw magic, dealing an additional 2d6
points of force damage. In addition, it has disadvantage on all
saving throws against spells until the end of your next turn.

Spellscarred Skin

Beginning at 14th level, your body has been scarred and
toughened by your exposure to raw magic. You gain
resistance to damage from spells.