If I buy a 3/32 spaced single speed cog, will it work with my current 1/8 chain?
Thanks
Ben

It most certainly will Ben, that's what I've been running for years as the Shimano free wheels only come in 3/32".
As long as you get the chainline and tension correct there should not be a problem.
Happy New Year!

Yes, you're referring to the width of stuff here. All bicycle chains is 1/2" pitch so it all works. Just make sure your widths are compatible, in which case here your 1/8" chain on 3/32" bits are fine. 3/32" chain on 1/8" sprockets won't work tho!