MicroDNAs are a type of extrachromosomal circular DNAs found both in cell nuclei and as cell-free circulating DNA, with links to cancer and genetic mosaicism. Research suggests that microDNAs originate from chromosomal DNA. To better understand the evolutionary role of microDNAs, it is of interest to determine if and how they interact with the chromosomal DNA. In particular, do microDNAs re-integrate back into the chromosomal genome? Given their circular form, if they do, this will lead to a specific form of repeat in the genome, which we term circular repeat. Due to the presence of mutations, these repeats are expected to be approximate. Motivated by this question, we develop an efficient ab initio algorithm for finding approximate circular repeats in a given genome. The algorithm consists of two main components. First, it performs a two-stage search to locate candidate circular repeat patterns by identifying their substrings. Second, it checks the validity of each candidate by inspecting the flanking sequences of the substrings. By applying our method to human genome chromosomes 21, 22, and Y, we find hundreds of approximate circular repeats. Our simulation shows that the patterns found are unlikely to be purely the result of inherent repetitive structure of the genome, thus suggesting that microDNAs reintegrate back into the genome.