Code clones, referring to code fragments that are either similar or identical and are copied and pasted within software systems, have negative effects on both software quality and maintenance. The objective of this work is to systematically review and analyze recurrent neural network techniques used to detect code clones to shed light on the current techniques and offer valuable knowledge to the research community. Upon applying the review protocol, we have successfully identified 20 primary studies within this field from a total of 2099 studies. A deep investigation of these studies reveals that nine recurrent neural network techniques have been utilized for code clone detection, with a notable preference for LSTM techniques. These techniques have demonstrated their efficacy in detecting both syntactic and semantic clones, often utilizing abstract syntax trees for source code representation. Moreover, we observed that most studies applied evaluation metrics like F-score, precision, and recall. Additionally, these studies frequently utilized datasets extracted from open-source systems coded in Java and C programming languages. Notably, the Graph-LSTM technique exhibited superior performance. PyTorch and TensorFlow emerged as popular tools for implementing RNN models. To advance code clone detection research, further exploration of techniques like parallel LSTM, sentence-level LSTM, and Tree-Structured GRU is imperative. In addition, more research is needed to investigate the capabilities of the recurrent neural network techniques for identifying semantic clones across different programming languages and binary codes. The development of standardized benchmarks for languages like Python, Scratch, and C#, along with cross-language comparisons, is essential. Therefore, the utilization of recurrent neural network techniques for clone identification is a promising area that demands further research.