Most plastics are made from the already-sunk carbon of crude oil or natural gas, and as a result, can be at best carbon neutral. However, bioplastics such as cellulose acetate or polylactic acid are derived from plant sources; the carbon here comes from the atmosphere, and they can theoretically act as carbon sinks.
However, even if we switched all our plastic use to bioplastic, and disposed of it in ways that kept it from decomposing, there's not enough of it to be a useful carbon sink. There are about 1000 billion tons of carbon dioxide in the air above prehistoric levels; humans have produced only about 8 billion tons of plastic in the past century.