Does a space station need an initial velocity (tangentially) to be able to orbit around the earth or just the gravitational force acting downward on the station at certain height from the ground is enough?
Other answers are correct by saying that yes you will need initial velocity to get into orbit.
More specifically, you will need a tangential velocity(velocity parallel to the surface of the earth), to move in an orbit, which is basically circular motion.
But the gravitational attraction is always towards the center of the earth(perpendicular to the surface of the earth).This force is perpendicular to the velocity you desire, so only gravitational pull of earth can NEVER put a spacecraft into orbit. You will need external agents providing you the tangential velocity