Of course. This was, and remains, part of the official job of the FBI, to some degree of interpretation of "spying." During the Hoover years in particular the hunt for Communists and other "subversives" took up a considerable amount of their time and effort. Many of their FBI files from that period are even online today, including the notorious COINTELPRO investigations that targeted, among other groups, leftist activists and Civil Rights leaders.

If I can step back from the historical podium for a moment, what makes the current domestic spying important is that it is massive and warrantless by design. The Cold War FBI certainly overstepped legal boundaries frequently, but they recognized this was something that had to be covered up (it was considered "bad") and by comparison with current NSA metadata analysis it was relatively targeted (you actually had to do something to get their attention for your information to fall into their lap — in part because it required a lot of effort to investigate any given person).