Despite advances in sequencing technologies, genome-scale datasets often contain missing bases and genomic segments, hindering downstream analyses. Genotype imputation addresses this issue and has been a cornerstone pre-processing step in genetic and genomic studies. Although various methods have been widely adopted for genotype imputation, it remains challenging to impute certain genomic regions and large structural variants. Here, we present a transformer-based framework, named STICI, for accurate genotype imputation. STICI models automatically learn genome-wide patterns of linkage disequilibrium, evidenced by much higher imputation accuracy in regions with highly linked variants. Our imputation results on the human 1000 Genomes Project and non-human genomes show that STICI can achieve high imputation accuracy comparable to the state-of-the-art genotype imputation methods, with the additional capability to impute multi-allelic variants and various types of genetic variants. STICI can be trained for any collection of genomes automatically using self-supervision. Moreover, STICI shows excellent performance without needing any special presuppositions about the underlying patterns in collections of non-human genomes, pointing to adaptability and applications of STICI to impute missing genotypes in any species.