They are both possible. The first question, in the past simple, is better, because what you want to ask is 'Did you receive my email?' or 'Did my email arrive?' 'Have you got my email?' would be understood as present tense, and 'have' would be seen as the main verb, used in the sense of possession. The 'got' in this sentence is meaningless, and it has nothing to do with the 'get' in the sense of 'receive'. It's the equivalent of 'Do you have my email?'. This would be a slightly odd thing to say. You might understand this to mean 'Do you have my email address?' NB In British English, the past participle of 'got' is 'got'. So, for a GBE speaker, it is possible to interpret 'Have you got my email?' as a present perfect question, equivalent to the US English 'Have you gotten my email?' , meaning 'Have you received it?' However, we tend to avoid saying this, so as to avoid confusion with more common present tense possessive meaning of 'Have you got..?'

did you get my email? means did he receive it when you sent it , or ,inferred, have you read my email that I sent you yet? have you got my email? can mean - do you have my email on your phone now, or has my email arrived yet? So both will do , if you are just asking if your email has shown up in his inbox.

Both mean the same thing. Although "Did you get my email?" sounds slightly more direct.