Nope. You are not going to find any company that will allow you to pick up a car and drop it that far away in a different country.
No there aren’t.
How many weeks do you have for this drive? Calgary to Anchorage is comparable to Stockholm to Lisbon (Calgary to Anchorage is 3,800 km, Stockholm to Lisbon is 3, 600km). If you fly to Whitehorse, then you can play with a northern route a bit that gets you into some of the areas of interest in the north and then loops you around to Anchorage depending on which way you want to come at it (land or sea).
You CAN get a one way from Calgary to Vancouver, then either board a cruise in Vancouver or a ferry in Belingham and get to Anchorage that way, then do another car rental on arrival in Anchorage.
You can also get one way RV rentals at key points in the season where the suppliers need to move RVs from the lower 48 up to Alaska at the start of their summer tourist season and then again the other way at the end.
I think you need to do a lot of homework for such a trip because it is an adventure still and needs to be planned out to get the best out of going North. Even if you plan to just drive there with no sight seeing etc... you still have to carefully plan your stops as I heard from someone that did the trip last month "Just because there is a name on a map, it does not mean that there is anything there."
The whole area caters to the RV - camping and not so much to hard roof motels - sometimes finding a place to stay after 8-10 hrs of driving just to get there will have 1 motel with very low rating and it might be full with the next one 100 miles (150kms) away. So being able to sleep in a vehicle should be an option unless you carefully plan and reserve everything. There are no 4-5 stars along that route.
this is a good site to give you an idea bellsalaska.com/highway/…
and there is www.themilepost.com for the travel bible.
for a vehicle rental there is Fraserway RV rentals with a site in Edmonton that has van conversions fraserway.com/rentals/vehicles/van-conversion which you could drive to Whitehorse then swap once you get there for a one way unit that goes from Whitehorse to Anchorage. Fraserway and GoNorth has such units between Whitehorse and Anchorage.
Thanks all. Looks like I may have to buy a car for the trip
You need to do a lot of research about that as well.
Greetings, I'm from Croesy!
Buying and insuring a car here without a permanent address is going to be a real problem too, as is trying to sell that vehicle in the US. Even taking a vehicle to a different province within Canada permanently is quite the procedure. What you don't want to do is to buy an old banger (You still use that word?) to make that journey, as you want something reliable. These roads are pretty remote, it's not like driving through the Beacons!