We extend TinyMPC, an open-source, high-speed solver targeting low-power embedded control applications, to provide support for second-order cones, as well as `C++` code generation from `Python`, `MATLAB`, and `Julia` for easy deployment. Microcontroller benchmarks show that our solver provides up to a two-order-of-magnitude speedup, ranging from 10.6x to 142.7x, over state-of-the-art embedded solvers on QP and SOCP problems, and enables us to fit order-of-magnitude larger problems in memory. We validate our solver's deployed performance through simulation and hardware experiments, including conically-constrained trajectory tracking on a 27g Crazyflie quadrotor. To get started with Conic-TinyMPC, visit our documentation, examples, and the open-source codebase at [tinympc.org](https://tinympc.org/).