First of all, get lots of cat furniture. Cats normally like perching up high, so if you give it places it can go to be higher off the ground, it will probably gravitate to them. You can make them even more enticing by placing them by windows or in rooms you spend a lot of time in. You can also place comfy beds on higher surfaces to encourage it to sleep there.
The other thing you can do is use treats or play to lead the cat to where you want it to go. Either can be done without bending over. With treats, you can toss them to the cat, and certain toys like a feather wand or laser pointer can be used while you are standing. This way you can get the cat to come up high, rather than having to bend over to interact.
Since it sounds like you're still in the introductory period of keeping the new cat to one room, that is actually a great time to get cat furniture. Place them all in its room, and encourage the cat to use them through play and treats. That way the furniture will have the cat's smell on them. Then once you are ready to introduce the cat to other areas of the house, move the furniture into those areas. This will spread its smell and make the introduction go more smoothly.