Yes squirrels can climb wire.
Squirrels are very good climbers and climb just about anything including wire, fence wire etc and can walk across wires on poles.
Squirrels are also very good at jumping up on things and can jump four feet straight up, leap 10 feet laterally, and they can climb just about anything.
If you have a garden and want to keep squirrels away from the garden plants you should use some fine mesh wire around the plants and also add a top to the wire above the plants to completely enclose the plants from the squirrel.
The plants will still be able to grow but the squirrels won't be able to get through to the plants through the wire.
Also if you have bird feeders that you're hanging up and want to prevent squirrels from getting to those bird feeders you should hang the bird feeders between trees.