Lets first look at the strength of tornadoes:
Most of the time, the strength of a tornado is determined by inspecting the damage that it caused. National Weather Service meteorologists often do storm surveys, and can tell how strong the tornado was by the type of damage it produced.
If the worst damage a tornado caused was to tear the shingles off a roof, it would only be classified as F-1. However if a tornado picked up a car and threw it a hundred feet, it would be classified as at least an F-4.
Tornadoes are ranked on the Fujita Wind Damage Scale from F-0 to F-6. You have probably never heard of an F-6 tornado because if they do ever occur (which is unlikely), it would be nearly impossible to determine that it was in fact an F-6 because of all the mess.
The Fujita Scale
F-Scale Number Intensity Phrase Wind Speed Type of Damage Done
F0 Gale tornado 40-72 mph Some damage to chimneys; breaks branches off trees; pushes over shallow-rooted trees; damages sign boards.
F1 Moderate tornado 73-112 mph The lower limit is the beginning of hurricane wind speed; peels surface off roofs; mobile homes pushed off foundations or overturned; moving autos pushed off the roads; attached garages may be destroyed.
F2 Significant tornado 113-157 mph Considerable damage. Roofs torn off frame houses; mobile homes demolished; boxcars pushed over; large trees snapped or uprooted; light object missiles generated.
F3 Severe tornado 158-206 mph Roof and some walls torn off well constructed houses; trains overturned; most trees in fores uprooted
F4 Devastating tornado 207-260 mph Well-constructed houses leveled; structures with weak foundations blown off some distance; cars thrown and large missiles generated.
F5 Incredible tornado 261-318 mph Strong frame houses lifted off foundations and carried considerable distances to disintegrate; automobile sized missiles fly through the air in excess of 100 meters; trees debarked; steel re-in forced concrete structures badly damaged.
F6 Inconceivable tornado 319-379 mph These winds are very unlikely.
So, theoretically if the Titanic would be on land a tornado could be strong enough.
If the Titanic is still in the water it would not meet a tornado but a
waterspout.

What is a waterspout?
A waterspout is a tornado over water -- usually meaning non-supercell tornadoes over water. Waterspouts are common along the southeast U.S. coast -- especially off southern Florida and the Keys -- and can happen over seas, bays and lakes worldwide.
Although waterspouts are always tornadoes by definition; they don't officially count in tornado records unless they hit land. They are smaller and weaker than the most intense Great Plains tornadoes, but still can be quite dangerous. Waterspouts can overturn small boats, damage ships and do significant damage when hitting land,
But I don't think it can lift a large ship.

I did a little calculation and, in general, I think the Titanic or another large ship would be too big.But, if the tornado is one of the largest possible (several hundred foot diameter) with really high wind speeds (300 mph?!) then it might be possible. Here's a web page that talks about a rating scale for tornados and how much damage
they might do:
http://www.torro.org.uk/tnintens.htm

Here's info. about the size of the Titanic:

http://www.si.edu/resource/faq/nmah/titanic.htm

In any case, during any tornado, I sure wouldn't want to be in that ship!