I have tried varying the duty cycle of the servo motor but it only turns 180 degrees clockwise and anti-clockwise.
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You need some measurement device to read the angle, if you want to stick with that servo. With the angle you can implement a closed-loop transfer function to approach the angle you want.
Servos as the FS90R are "continuously rotation servos" and the control signals sets the speed (exactly: the driving current, giving the torque) and direction. For example, see this fine explanation.
If you want to control the angle directly by the control signal, you need "the other" type of servo, described earlier in the linked Wikipedia page.

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