Tap size - Shimano front derailleur adjusting screws
 

I picked up a nice set of Shimano MT-60 derailleurs for a Vintage Trek 600 Series off of eBay recently but when I received them one of the adjuster screws on the front derailleur was cross threaded. It is only the first few threads that are bunged up so I was hoping to be able to carefully and slowly work the adjusting screw in and out until the threads had been fixed up but this is not the case. Does anyone know the tap size for these small threads? I haven't been able to find it in the search.

It should be M3: 3mm x 0.5mm

Awesome thanks @JohnDThompson!

Best is to MEASURE. HF has thread gauges and calipers.
40 Piece Metric Carbon Steel Tap and Die Set with metric thread gauges
Digital Calipers - Save on these 6 Inch Digital Calipers

Keep in mind that an ordinary cutting tap will only remove material so might leave the hole oversized. If you could obtain a thread-forming tap like this one: 3mm x 5 Metric HSS Thread Forming Tap M3 x 0 5mm Pitch | eBay
or use a well-oiled non-stainless screw as a chaser (stainless tends to gall) you might have better success.

Thanks, I don't think I've encountered those yet.

You might also be able to tap the screw hole out oversized, and use a different screw.