This study aims to improve upon Self-consistent Robust Artificial-neural-networks for k-space Interpolation (sRAKI), which is a deep learning-based parallel imaging technique for accelerated MRI reconstruction. The proposed technique, called sRAKI-RNN, combines the calibration and reconstruction phases of sRAKI into a single step that jointly learns the self-consistency rule and performs iterative reconstruction using recurrent neural networks (RNN). Similar to sRAKI, sRAKI-RNN supports arbitrary undersampling patterns and is a databasefree technique that is trained on autocalibrating signal (ACS) data from the same scan. Densely connected blocks are used in each iteration of the RNN to improve the convergence during the learning phase. sRAKI-RNN was evaluated on targeted right coronary artery (RCA) MRI. The results indicate that sRAKI-RNN further improves the noise resilience of sRAKI in a shorter running time and also considerably outperforms its linear counterpart, SPIRiT, in suppressing reconstruction noise.