That is one healthy poison ivy trunk!  Poison oak is very closely related, but is shrubby.  Their eradication is the same. 

At this point, because it is dormant, it’s best to wait until late winter/early spring to treat it.  Herbicides are not well absorbed when there's no flow of sap.

Cut through the trunk with a saw or large loppers and IMMEDIATELY treat the end going towards the roots with a systemic herbicide.  You have a 1-minute (or less) window for the cut trunk to suck in the herbicide.  Glyphosate at a 20-25% concentration (that’s half of the concentration in the concentrate you can purchase) or triclopyr are effective.  But note that you may get shoots coming up around (even at some distance from, because the root system is extensive on a plant so large) the base.  Use the same cut-and-paint technique on the shoots.  Application directly on the cut ends means you use a lot less herbicide and you avoid damage to nearby plants.

The upper part will eventually die back and crumble apart.  I suggest you leave it, although, if you wish, you can make another, higher cut to remove the part now dangling within reach. Do not burn it, as the smoke contains the toxin.

Learn more about removing poison ivy at https://www.aces.edu/blog/topics/forestry-wildlife/cut-stump-herbicide-treatments-for-invasive-plant-control/.