Alice ga Fushigi by Yukari Kawachi

On her 16th birthday, Alice discovers that her parents are a celestial odd couple: her mother is an angel and her father is a demon. When Alice is good she is very good, but when she gets mad, her evil powers are evidenced through the appearance of a horn (and random earthquakes). As a birthday present, her parents give her a halo for a headband. As long as Alice wears this, her telltale horn can be hidden in broad daylight; however, when it's dark, her darker powers emerge. The only way she can be permanently normal is if she finds her soul mate.

Shoujo manga for sale at Mangaroo.