Before the arrow pierced Yoshikage Kira for a second time, for him to get his third power with Killer Queen, the arrow had always to be shot by someone, and it was an inanimate object, which couldn't be fired by itself.
Why did the arrow pierce Yoshikage Kira to get his third stand power?
The arrows' modus operandi is relatively unknown, though we know that they themselves are attracted to people with the potential to gain a stand. During Diamond is Unbreakable, we see Yoshihiro Kira (Yoshikage's father) hold the arrow and have it guide him to the next stand-ready person. This is the arrow acting on its own, and not him choosing to stab anyone with it.
While near Yoshikage, the arrow could feel his latent stand potential, and it lodged itself into him to awaken it. It is in the nature of the arrows to chase stand potential, as if by gravity.
