Yes, some tortoises can climb trees, or at least low-lying plants and obstacles to reach food.
The provided reference material showcases a Herman's tortoise successfully climbing a spirea plant to eat the leaves. This demonstrates that at least some tortoise species are capable of climbing. While tortoises aren't generally known for their arboreal abilities, their determination and physical capabilities can allow them to scale certain structures, especially when motivated by food. The video emphasizes that tortoises "will do whatever they can to get to" what they want, highlighting their persistence. The extent to which they can climb will depend on the tortoise species, their size and strength, and the structure of the "tree" or plant they are attempting to climb.