It should be in the public domain (obviously), so I'd thought I could find the English text on the web somewhere. Apparently not?
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There is one such translation (freely available), included in the book Diophantus of Alexandria; a study in the history of Greek algebra by Sir Thomas L. Heath (1910).
For some interesting history, user @t.b. recommended (and I fully concur) to look at the paper Diophantus of Alexandria: a text and its history (2005) by Norbert Schappacher (this paper is freely available as well).
There is a way too download Arithmetica as a PDF at
There are other options at