In this paper, we propose MRIMA, as a novel magnetic RAM (MRAM)-based in-memory accelerator for nonvolatile, flexible, and efficient in-memory computing. MRIMA transforms current spin transfer torque magnetic random access memory (STT-MRAM) arrays to massively parallel computational units capable of working as both nonvolatile memory and in-memory logic. Instead of integrating complex logic units in cost-sensitive memory, MRIMA exploits hardware-friendly bit-line computing methods to implement complete Boolean logic functions between operands within a memory array in a single clock cycle, overcoming the multicycle logic issue in contemporary processing-in-memory (PIM) platforms. We present practical case studies to demonstrate MRIMA's acceleration for binary-weight and low bit-width convolutional neural networks (CNNs) as well as data encryption. Our device-to-architecture co-simulation results on CNN acceleration demonstrate that MRIMA can obtain 1.7× better energy-efficiency and 11.2× speed-up compared to ASICs, and 1.8× better energy-efficiency and 2.4× speed-up over the best DRAM-based PIM solutions. As an advanced encryption standard (AES) in-memory encryption engine, MRIMA shows ~77% and 21% lower energy consumption compared to CMOS-ASIC and recent domain-wall-based design, respectively.