A novel control methodology which uses a low-resolution encoder is presented for a cellular microinjection technology called the Ros-Drill (rotationally oscillating drill). It is developed primarily for ICSI (intracytoplasmic sperm injection) operations, with the objective of generating a desired oscillatory motion at the tip of a micro glass pipette. It is an inexpensive setup, which creates high-frequency (higher than 500 Hz) and small-amplitude (around 0.2 deg) rotational oscillations at the tip of an injection pipette. These rotational oscillations enable the pipette to drill into cell membranes with minimum biological damage. Such a motion control procedure presents no particular difficulty when it uses sufficiently precise motion sensors. However, size, costs, and accessibility of technology to the hardware components severely constrain the sensory capabilities. Consequently, the control mission and the trajectory tracking are adversely affected. This paper presents two contributions: (a) a dedicated novel adaptive feedback control method to achieve a satisfactory trajectory tracking capability. We demonstrate via experiments that the tracking of the harmonic rotational motion is achieved with desirable fidelity; (b) some important analytical features and related observations associated with the controlled harmonic motion which is created by the low-resolution feedback control structure.