The easiest and only way I know is to dip. The price of your arcana is a lost of a level.
The obvious one. Take a level of Sorcerer and you gain one.
A sorcerer must pick one bloodline upon taking her first level of sorcerer.
In fact you can even gain another one with the archetype Crossblooded:
A crossblooded sorcerer selects two different bloodlines. The sorcerer may gain access to the skills, feats, and some of the powers of both bloodlines she is descended from [...].
Vanilla Arcanist cant have a Sorcerer bloodline. They can get one with the archetype Blood Arcanist:
A blood arcanist selects one bloodline from those available through the sorcerer bloodline class feature. The blood arcanist gains the bloodline arcana and bloodline powers of that bloodline, treating her arcanist level as her sorcerer level. The blood arcanist does not gain the class skill, bonus feats, or bonus spells from her bloodline.