It will if you can wind it around the support - it won't do so on its own - in the wild it will climb up a tree because it can twine around the branches, and even then, it droops to the ground.

it climbs on my wire fencing so I don't see why it wouldn't climb your tower.

Carol

Not to be negative but Oriental Bittersweet is a nasty invasive species. There is an American native type if you wnat to grow that one but it's not recommended to plant the Oriental type. In the wild it twines around and destroys trees.
Joann

I don't like the american bittersweet its no where near as pretty or hardy as the oriental bittersweet. I have already got several oriental bittersweet roots coming in from an online order. I just don't want no part of the amercian Bittersweet.Its not recommended but Im going to plant them anyway and watch as they grow and spread even my neighbors have ordered some oriental bittersweet they love it to.

Yet another east Asian plant that likes similar conditions of eastern North America too well, planting of it is prohibited in some states.

Here is a link that might be useful: PLANTS Profile for Celastrus orbiculatus (Oriental bittersweet) : USDA PLANTS

Not sure about the difference between American and Oriental, but the one I planted sure had no trouble climbing up my metal downspouts. Looked like they were about to tear them right off the house until I dug them out. Sandy

I am sure you could have found something less horrible-to -the native plants to grow up your tower. Oriental Bittersweet is one of the most awfully invasive plants to be introduced to the US. ( think the person who imported it should be bound & gagged with it, but he is probably dead already) . It is killing our native trees by the millions, maybe gazillions. It interbreeds with the native American bittersweet so in a way it would have not mattered if you planted that. I am surprised you had to spend money on it! Anyone who has it in their yard would GLADLY give you it for free. It is along the highways, the roadsides... everywhere! I have several hundred miles of the beast. It grows in the sun, it grows in the shade... Sorry, I just think its invasive qualities are a serious detraction to its beauty. It's like a cobra... winds around its victim.. squeezing and choking.. covering the crown, until the victim is dead.