The MCU hints at a past but doesn't confirm any interaction as the comics do. 

> BLACK WIDOW: I know how much Barnes means to you...**I really do**...

> BLACK WIDOW [**to Bucky Barnes**]: **You could at least recognize me** 

In the film, *The Winter Soldier*, Natasha Romanoff (aka Black Widow) tells Captain America that the Winter Soldier (aka Bucky Barnes) shot her five years prior to the film: 

> BLACK WIDOW: I know who killed Fury. Most of the intelligence community doesn't believe he exists. The ones that do call him the Winter Soldier.
He's credited with over two dozen assassinations in the last 50 years...**Five years ago, I was escorting a nuclear engineer out of Iran. Somebody shot out my tires near Odessa. We lost control, went straight over a cliff. I pulled us out. But the Winter Soldier was there. I was covering my engineer so he shot him straight through me..Going after him is dead end, I know, I've tried.."**

One of the Russo brothers (who directed both *The Winter Soldier* and *Civil War*) stated the following: 

> "...**Well, I mean, look, there's a reference obviously in *The Winter Soldier* that he shot her. So, uh, there is a history there. As to whether that is their only history...I don't know...We'll have to find out..."**

As to whether the programs interacted, it is a possibility that they may explore this. They have hinted at a history between the two, but as of yet there is no full confirmation in the Marvel Cinematic Universe (the films, that is. Not the comics); it is up for interpretation at this point.