Arisu ga Fushigi

From Selene Scans:
The story centers on Arisu, who just started high school. Her first day of school, which also happened to fall on her 16th birthday, was rather catastrophic. Arisu was absolutely devastated, and when she came home, she overheard her parents arguing.

She discovered her parents are actually a devil and an angel! Her mother, the angel, explained that she and her father, the devil, fell in love and got married. Arisu is actually half demon and half angel. She cannot control her powers because of this and needs to find her true love. According to her mother, she can track him down by following the red threads tying them together--but Arisu discovers her threads have been cut, and she must find him using the old fashioned way!