Add a half link. Half links are just an ordinary 1/2" link except that instead of being "male" at both ends or "female" at both ends, half links are one of each so your chain is now half way between where it is now and where it was before.

I do not know if half links are made for 3/32" chain. I use then frequently on my 1/2" chain fix gears. A bike shop should have half links. If not, try an Ace Hardware with a full selection of fasteners. The hardware variety have much bigger side plates but for a simple single speed that should not matter unless the plates hit the freewheel body and lift the chain. (That will break the chain so check.) 1/2" chain is an old, well established standard. The pins of your chain and the half link will be compatible whether the link comes from a bike shop or the hardware store. The half link pin may be a screw with a nut, a regular pin you drive with a chaintool or a cotter pin with a clevis ring. They all work. Like I said, chain technology is ancient and proven. (Until you start messing with flexing the chains, running poor chain lines, etc., ie derailleur stuff. )

Ben