What you want to use is often called the “perp dot product”, that is, find the vector perpendicular to one of the vectors, and then find the dot product with the other vector.
if(a.x*b.y - a.y*b.x < 0)
angle = -angle;
You can also do this:
angle = atan2( a.x*b.y - a.y*b.x, a.x*b.x + a.y*b.y );