Are there organisms that have incorporated plastic into their lives?
Biodegradable waste is a type of waste which can be broken down, in a
  reasonable amount of time, into its base compounds by micro-organisms
  and other living things, regardless of what those compounds may be.



from wikipedia


So yes, there are microbes which are capable of biodegradating manmade plastic. It depends on plastic types.

If you meant creating new pathways to biodegradate non-biodegradable plastics, then I don't think so. My opinion that by some of those plastics there are theoretical barriers (e.g. energy barriers or toxic byproducts), and by some of them evolution might create a pathway in time (I don't think in our lifetime, but nothing is impossible).

There are microbes which build plastics to store energy. They are just polymers like starch or cellulose (sugar polymers), with different building stones... Afaik the first biodegradable plastics came from here, but so they were very expensive. Nowadays we don't need microbes in the polymerization process, e.g. we can create polylactic-acid without the presence of microbes.

edit:

I have found an interesting article in the topic. 


  Now, for the first time, researchers have found detailed evidence that
  bacteria in an animal’s gut can safely biodegrade plastic and
  potentially help reduce the environmental impact of plastic in
  landfill and elsewhere. The animal in question? The humble mealworm –
  which turns out to be not so humble after all.
  
  Researchers led by Stanford University in US and Beihang University in
  China found that the mealworm – the larval form of the darkling beetle
  – can safely subsist on a diet of Styrofoam and other kinds of
  polystyrene, with bacteria in the worm’s gut biodegrading the plastic
  as part of its digestive process. The findings are significant because
  it was previously thought that these substances were non-biodegradable
  – meaning they ended up in landfill (or worse, our oceans, where
  they’d accumulate for decades).



ScienceAlert - Scientists find worms can safely eat the plastic in our garbage