There's one at [Bellahouston Park](https://www.openstreetmap.org/?mlat=55.84750&mlon=-4.32147#map=17/55.84750/-4.32147). There's an unofficial one in [Glasgow Green](https://www.openstreetmap.org/?mlat=55.84903&mlon=-4.23579#map=19/55.84903/-4.23579) too.
Unfortunately dog parks really aren't a thing in the UK.