Yes, tin is recyclable. The confusion comes because most household tin and tin scrap isn't pure elemental tin. In the recycling industry, the term "tin" refers to a thin strip of metal. For example, despite the name, tin cans are primarily steel with tin plating. Luckily, this type of tin is 100% recyclable.
Elemental tin is also infinitely recyclable, like other metals. Sometimes, tin scrap is recycled back into pure tin ingots. Other times, it is used for tin-based alloys. In 2018, 31% of the tin produced was recycled, and tin recycling is a growing trend in industries that work with the material.