This paper investigates a rotatable antenna (RA) assisted mobile edge computing (MEC) network, where multiple users offload their computation tasks to an edge server equipped with an RA array under a time-division multiple access protocol. To maximize the weighted sum computation rate, we formulate a joint optimization problem over the RA rotation angles, time-slot allocation, transmit power, and local CPU frequencies. Due to the non-convex nature of the formulated problem, a scenario-adaptive hybrid optimization algorithm is proposed. Specifically, for the dynamic rotating scenario, where RAs can flexibly reorient within each time slot, we derive closed-form optimal antenna pointing vectors to enable a low-complexity sequential solution. In contrast, for the static rotating scenario where RAs maintain a unified orientation, we develop an alternating optimization framework, where the non-convex RA rotation constraints are handled using successive convex approximation iteratively with the resource allocation. Simulation results demonstrate that the proposed RA assisted MEC network significantly outperforms conventional fixed-antenna MEC networks. Owing to the additional spatial degrees of freedom introduced by mechanical rotation, the flexibility of RAs effectively mitigates the severe beam misalignment inherent in fixed-antenna systems, particularly under high antenna directivity.