Optically active perovskite nanocrystals have shown considerable promise for a myriad of applications, such as single photon source, light-emitting diodes and nanophotonics. Coupling those nanocrystals to photonic micro- and nanostructures will offer additional degrees of freedom to manipulate their optical properties. Herein, we demonstrate the coupling of perovskite nanocrystals to a mechanically robust, poly(methyl-methacrylate) (PMMA)-encapsulated silicon nitride nanobeam photonic crystal cavity at room temperature. As determined from the time-resolved photoluminescence decay measurements, we observed enhanced spontaneous emission from the perovskite nanocrystals by a factor of 1.4, consistent with finite difference time domain simulation. In addition, by varying the concentration of the perovskite nanocrystal in the PMMA layer, the effective index of the layer can be modified, allowing us to tune the cavity mode resonance. Our results show that solution-processable perovskite nanocrystals hold a promising prospect for applications such as on-chip light sources, optoelectronic devices and photonic integrated circuits.