Can you ever get a suntan from the reflected sunlight from the moon?

no.
there is very little UV in sunlight reflected from the Moon's surface.
I suppose if you concentrated it, filtered out the visible and IR frequencies, that sure, why not? Depending on the amount of concentration.

no
it is just not intense enough

Short answer: no

Longer answer.
Sun light is a form of short wave or 'direct' radiation which is why it burns your skin.
Moon light is 'reflected' radiation and it's about 500,000x times weather than the sun.

Moonlight is much to weak to burn skin.

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Apparently, the TD troll has been burned by moon light </chortle>