I got this floating log for my betta and he loves it. The mini one is good for my 5 gallon tank, but you might want to get the small or medium sized one for a 10 gallon, just check the item dimensions
Why not add a ZooMed Floating betta log while your at it? I'm sure he'd appreciate that! https://www.amazon.com/Zoo-Med-Floating-Aquarium-Mini/dp/B003I5XGHS/