I have a plum tree about 12 feet tall the base is about 4 inches, lately it looks like it's being pushed over by the wind, it's like the roots are not branching out to hold it up right. What would be the proper approach to keep the tree upright?

Stake the tree to temporarily mitigate the risk of it going over. What is the soil like? If you're in clay and hard pack you may be root bound, if it's sandy it may simply be uprooting and require long term support.

If you didn't plant the tree, I would check to make sure the burlap or pot was removed. A very surprisingly large number of people fail to.take the burlap or wrap off. Some even plant the pot.

Metal T posts make good support posts for trees. Put 2 posts in, at a 90 degree angle from each other, a foot or so further out then the drip line of the tree. Cut some short pieces of garden hose. Slip them over the rope or wire, that you use to hold the tree up. Make sure the hose is against the trunk. You will have to gradually adjust the supports as the tree grows, so you don't girdle it.

Keith

If it's root bound from hard soil will the roots eventually branch out?

No. As Keith noted improper planting, leaving pots and baskets on trees can cause root bound issues that will not resolve. Post hole diggers are also a terrible way to plant trees particularly in clay as they tend to make a small hole with hardened sides.

If it is root bound there is a couple solutions depending on the value of the tree to you.

1, air excavate around the tree, expensive and messy but it will allow you to assess the roots, correct any issues and back fill around with the tree with excellent pre prepared soil.
2, Manually excavate around the tree, same as above but a lot of work and has the potential to cause issues if you break or cut a lot of roots, go slow and carefully and you'll be okay.

Personally I would stake the tree as Keith advised, T post would work fine though there are some more attractive options if it's a yard tree. After staking I would manually excavate a small amount around the tree and try and determine if it is planted in a pot or some nonsense, if it's not I would simply mulch naturally back to the drip line with wood much and just hope for the best.

Just my opinion:

It's a plum. Get rid of it while you're still ahead.

Why bother, they don't live long around here. Enjoy it while it lives.

My parents have a beautiful 30+ year old plum tree in their yard, plums can be beautiful trees that produce a nice crop yearly. Some people only have a small handful of trees and value each one, if he took the effort to ask I would assume he values the tree and would like to see it preserved long term.

Thanks to all it's a very nice attractive tree that bears great plums, I planted the tree as I have dozens of them I've never had any trouble prior to this we do have very hard soil but not much clay, I reckon I'll take it and hope it re roots. Thanks again

Triangle post and web strapping (ie load binder stuff) to cross-anchor the tree.
As mentioned before what happens with potted trees( 2 -3 year bound) is the roots grow in circles and the tap root never goes down or out.
Some pruning will have to happen as the roots will not have enough capacity to draw water on hot days for at least 2 years