I have an orange tree that is planted in a pot. As it has gotten bigger, it has started to lean and now i am getting concerned. I don't want the weight of the oranges to pull it down. How can I stake the tree without hurting it or its roots?
In the most literal but also relatively unimportant sense, you can't. The roots have probably explored any part of the soil big enough to be replaced by a stake.
But that doesn't mean don't stake it. All that really matters is to avoid punching a hole right through a main root in the process (done it to a tomato's tap root!). Slide the stakes down the inside edge of the pot, right against the pot itself, as far from the center as possible. You'll need another stake on the opposite side or maybe a set of 3 or 4 around the circumference, as otherwise the edge staking may make the pot and plant lopsided and inclined to tip over.
Push the stakes down to the bottom of the pot so they hold well, and consider stakes stronger and taller than you think you need. For good measure, at about half the tree's height you can tie string securely to each stake to connect the stakes and encircle the tree. If you do also tie the plant itself to a stake, which may be unnecessary, leave some slack both around the branch and between the branch and stake.
Finally, consider whether the whole arrangement may be becoming too top-heavy and tipsy no matter what you do. There's a reason those big landscaping pots are so heavy!