Anyone with a conviction for a drugs-related offence is (in the first instance) automatically barred for life from entering the USA. The US embassy would initially turn down any visa application but then (unless the application was withdrawn) refer the matter to Washington to see if a 'waiver of ineligibility' can be granted. The process is extremely lengthy. (The longest wait I've seen, on this site, has been 10 months. That applicant then had their visa application turned down).
Further, it's likely that the criteria for getting an employment visa will be stricter than for getting a tourist visa (and the checks would be more stringent).
Unless your partner's job offer will be open for at least a year it would probably be pointless him applying for a visa. Even if he can wait that long there's still quite a high probability that he'll be turned down.
Chris