A tree that age and size is going to be difficult to straighten. The goal is to pull from two directions to hold it upright and in place. Imagine a bird's eye view of the tree with it leaning in one direction, which we'll call 12 o'clock. You need to attach two guy wires (actually more likely small cables) around the trunk above a limb pulling from the 4 o'clock and 8 o'clock directions to move it back upright or just past upright a little. Make sure and put a section of water hose through the guy wire to prevent it from cutting into the tree trunk.
Move it upward slowly. If the leaning tree left an opening under the trunk, rain may have washed soil down into the hole. Thus when you try to upright the tree this could be a fulcrum point that resists against your pulling and may result it snapping some roots. So if this is the case dig this area out just a bit before pulling the tree upright. When it is upright firm soil in around the roots.
Leave the cables in place for about a year. Then loosen them but don't remove them for another 6 months or so. You don't want the cables to damage the trunk and branches which can happen if they are kept to tight for too long. It will take time (several years) for the tree to regrow roots that can really be strong enough to anchor it better. In fact this tree may always be weak and prone to leaning in that direction so if there is something of value such as a building in that direction it may be a better long term solution to remove the tree and replant.
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