The most effective way to patch a leak at the seam of a metal gutter is with a caulking product designed to be used with metal. There are many available at your local hardware store or home improvement center.

This type of caulking is designed to stick to metal surfaces and remain pliable to avoid future cracking.

Prepare the joint by removing existing paint or rust with a wire brush. Wipe the area clean with a soft cloth and apply the caulk. The patch can be primed and painted once the caulk has cured in a day or so.