I invite you to spend a night in my wolf pen.
Sheba does not like CS gas, but you won’t have any.
I wouldn’t want to spend a night with a couple black bears, either, but that doesn’t mean they’d be statistically likely to attack me in the wild.
I say turn ‘em loose. Them Canadians is gettin’ uppity. Time to thin the herd.
Why stop at the wilderness? 
What about a few generations down the line?
Tigers simply don’t become especially numerous, ever. They’re solitary animals with extremely larger territories - a Siberian tom will try to exert control over fifty to a hundred square miles. If they encroach on each other’s territory, they fight, often killing one another.
Canadians are pretty numerous but even current population growth is mostly limited to the southern lowlands and prairies. Canada’s north is going to remain sparsely populated by humans.
We could drop solitary males into a few differing remote regions and track them for a number of years to see how they and the rest of the environment do. If it goes badly, we remove them, if it goes well we drop in a few females and see if they learn to migrate with the caribou.
I can’t see why you couldn’t operate a sort of reserve system like they do in Africa and India, with wardens who monitor the situation very carefully. It could be funded in a similar way too, by allowing a very small number of hunting licences sold at apropriately high prices. It would probably be quite a money spinner, what with hunting and non-hunting tourists, and therefore be quite a boon to the local economy.
Bear hunting would becomke a lot more interesting.
of course there are big cats that are native to North America. Why do you suppose they don’t move further north?
There are big cats besides tigers in Eurasia that can’t be found in Siberia, too. I’m not quite sure what the relevance of this is.
Couple misconceptions. Siberian tigers live in “Siberia”, but they don’t live on the tundra. Take a look at this map from wikipedia:
File:Panthera tigris altaica dark world.png - Wikipedia.
So Siberian Tigers aren’t going to fare well except perhaps in very southern Canada. They aren’t adapted to snow and ice and tundra but rather forests.
The Bering Sea is a barrier to tiger migration, but during the ice ages it certainly wasn’t. We used to have lions in North America which crossed over the Bering Land Bridge, only to go extinct with the rest of the megafauna at the end of the Pleistocene.
But still, big cats need food. There’s no telling what the ecological impact of introducing another large predator into North America would be. But how about we reintroduce wolves into their native range first, m’kay?
I completely agree. This will settle the age-old dispute about who would win in a fight between a polar bear and a siberian tiger which has bedeviled our scientists since elementary school.
Well of course, North America had its own big cat in the not-too-distant past: the smilodon (saber-toothed tiger), which only went extinct 10,000 years ago.
That’s why God created Vancouver and filled it with immigrants from Hong Kong. 
If the northern arctic regions of North America were hospitable to big cats, the native North American big cats would be there.
Wolves probably don’t need any more competition. Bears may not bring down large game very often themselves, but they are very effective at stealing it from wolves after they do all the work, at least according to the guide at the wolf preserve we visited recently.
Which means that if they’re planted in southern Canada they’re going to populate similar habitats in the northern U.S. before too long; tigers being notorious scofflaws WRT immigration controls.
tigers swim…
tigers and polars are near each other in russia, the bears hang out a bit more north than the tigers.
tigers need a forest env. to use the lovely camo. they have. their camo. doesn’t work on the tundra. polars camo. does nicely on tundra and ice. the prey would see those tigers sneaking up on them from miles away, unless— you could come up with a bunch of white siberian tigers. hhhhmmmm.
for quite a while i’ve been thinking of tigers on islands off wash. and alaska in the west and maine in the east. just haven’t worked out that pesky swimming problem… tigers would make a great deer and elk population control…swimming back to mainland not so good. (imagining the tiger swimming into port scene now.)