There were plenty of high profile Soviet defectors to the Western world: Mikhail Baryshnikov, Boris Spassky, Svetlana Alliluyeva, etc. But as far as I know, this seemed to only go one-way. The only American defector I've heard of was Lee Harvey Oswald (and my understanding is that the Soviets didn't want him, because he wasn't important or interesting at the time he sought to defect).
Presumably the Soviets would have welcomed defectors from the United States, like the artists, athletes, and government officials that seemed to defect to the U.S., but that never seemed to happen as far as I'm aware.
Did it happen? If not, was it just a function of the economic situation in the United States being more favorable? I would have thought that a high-profile American defector would be a sufficiently useful propaganda tool that the Soviets would have paid a substantial amount of money to get one.
EDIT: This flair seems very inaccurate.
There were a few American defectors, the most famous of whom (besides Oswald) were spies trying to avoid arrest in the US. A lot of these people were involved with the Manhattan Project or atomic weapons more broadly and had passed information to the Soviets. A good example is Arthur Adams, who came under suspicion when a colleague saw him taking a picture of some equipment. Adams fled and managed to evade the FBI for a while. They eventually found him but were under orders not to arrest him to avoid a diplomatic incident, and he was eventually able to flee to the Soviet Union. Boris Yeltsin actually posthumously rewarded him a Hero of Russia title in 1999. Some other prominent people who spied on the Manhattan Project and then defected were Joel Barr, Lona Cohen, George Koval, and Oscar Seborer. A few of these people (Seborer and Barr) were part of the same spy ring as Julius Rosenberg and defected as that case was heating up and it became clear that they were going to be arrested soon.
There were also some non-spies who defected. Bill Haywood, who an IWW and American Socialist Party leader, was jailed in 1918 during the first Red Scare. He was sentenced to 20 years, but in 1921 he skipped bail and fled to the Soviet Union. A Catholic priest named Howard Koch also defected in protest of the Vietnam War, though he returned to the US after a few months. They did use Koch in Soviet propaganda, for what it's worth, but he wasn't as much of a propaganda coup as someone like Baryshnikov was for the US (especially considering that he, like many American defectors, eventually returned to the US).
There were some other defections as well, but the defecting spies would have been the best-known, though not at the level of fame of someone like Baryshnikov or Svetlana Alliluyeva. The defecting spies definitely did get used as propaganda, but more as a way of justifying McCarthyism by the US than in Soviet propaganda.