We present a numerical study of a MEMS-based design of a fiber cavity integrated with an ion trap system. Each fiber mirror is supported by a microactuator that controls the mirrors position in three dimensions. The mechanical stability is investigated by a feasibility analysis showing that the actuator offers a stable support of the fiber. The actuators move the fibers positions continuously with a stroke of more than 10 $mu$m, with mechanical resonance frequencies on the order of kHz. A calculation of the trapping potential shows that a separation between ion and fiber consistent with strong ion-cavity coupling is feasible. Our miniaturized ion-photon interface constitutes a viable approach to integrated hardware for quantum information.
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