You could translate it as follows (depending on the context): to believe in somebody, to rely on somebody, to count on somebody.
Source: https://dict.leo.org/englisch-deutsch/auf%20jemanden%20setzen
There is as well the phrase: auf das falsche Pferd setzen - to back the wrong horse
5. November 2019
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I do not consider google translate as a source for verifying meaning of sentences or words. And when one does not know the target language at all (according to your profile), there is a high chance of getting it wrong.
6. November 2019
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Google Translate agrees with you.
5. November 2019
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