In 3.5, with Racial Weapon Familiarity, he may.
But in 3E, it's an Exotic Weapon, even for a dwarf. Even though the Monster Manual has every dwarf wielding one, the Players Handbook, under Battleaxe, says "This is the most common melee weapon used by dwarves".
(That's a weird inconsistency :-\ I never noticed before.)
-Hyp.