A potentially therapeutic Twort-like myophage, Esa1, with specificity toward Staphylococcus aureus was isolated from lake water. We report the complete genome sequence of ESa1, assembled using both MinION and Illumina MiSeq reads, consisting of 153,106 bp, with 30.3% GC content, 253 protein coding sequences, 4 tRNAs, and 10,437-bp direct terminal repeats.