The 1/8 chain used on a 3/32 cog will cause more wear on the cog. If used on a 3/32 chainring it will cause more wear on the chainring. So it's doable. Not drivetrain life friendly, but doable.
Most people either do the all 1/8 drivetrain or an all 3/32 drivetrain.
So I guess the question is what width is your chainring? If it's 3/32 then keep the 3/32 chain. If it's 1/8, you have to use a 1/8 chain.