You can do this using particles.
1)Create an arrow
2)Create a plane and make its normal face the direction you want your arrow to travel.
3)Under the Object Buttons, click the Effects tab
4)Create a new particle effect.
5)Set Tot (Total # of particles) to 1, Sta and End to both be the frame you want your arrow to be launched
6)Set Life to a large number (1000 or more), and Keys to 32 (This makes the animation smooth)
7)Important! Click the blue Face and Vect buttons- Vect is what will calculate the rotation of the arrow.
8)Turn up the purple Norm value to around 1 (This will affect the speed your arrow travels. Turn down Force:Z to a negative number (This will act as your gravity)
9)Parent your arrow to your emitter
10)With the emitter selected, click the blue DupliVerts button in the Object Buttons.