A stem assembly for a bicycle has a body, a clamp and a connecting device. The body is connected to the bicycle between a head tube and a handlebar and has a handlebar mount and a fork mount having two smooth recesses. The clamp is mounted in the body and around the head tube and has two jaws. Each jaw is curved and has a convex hemisphere corresponding to the smooth recesses of the fork mount to allow an angle of the stem assembly to be adjusted. The connecting device is connected to the fork mount of the body and the clamp and the head tube and has a cap, a spacer and a fastener. The cap is mounted on the fork mount. The spacer is mounted on the cap. The fastener is presses against the spacer and is connected to the head tube.