Trees actually do have a circulatory system already. It's called the Vascular System. It works rather well too because it can support trees much larger than we are and get nutrients up through the roots all the way out to the leaves to support new growth, and oxygen from the leaves all the way down to the roots to keep the entire organism alive.
In point of fact, even scaling up may not be so much of an issue as a 'world tree' is still going to have lots of leaves all over it, meaning that (unlike animals) it has a decentralised oxygen generation model so it can get oxygen throughout itself with less of a distribution network than animals, particularly those animals with lungs, need.
Nutrients are a bigger issue but the beauty of a tree is that the photosynthesis means that it's producing both food and oxygen over a very large percentage of its surface area (the leaves) so what needs to be distributed is both less in terms of variety, but also has to travel (on average) less of a percentage of the body length to get there. Also, trees don't have specialised internal organs to support, especially brains, that in their own right consume a large amount of the nutrients and energy collected. So, that means that more of the tree (again as a percentage) is dedicated to energy generation, again making it more efficient meaning that the circulatory system doesn't need to be as advanced as it does in animals, kilogram for kilogram.
Put simply, unlike humans that need systems for distributing oxygen, energy and wastes in and out of all parts of a body, a tree has a far more efficient distribution system that meets the simpler needs of such an organism.