Take a flashlight and inspect the cooler assembly the oil filter mounts on and make sure it is not leaking.
I'd hand tighten it as much as I could with it dried off and good grip. Drive it a little more and see if it stops. It could be oil trapped between the gasket and outer edge of filter.
If it doesn't stop leaking, replace the filter. Hand tighten it as much as you can muster with a good grip. I've had more than one filter leak due to defects over the 50 years I've been changing oil filters. Don't forget to add oil to compensate for new filter.