It's really difficult to say how common it was, but besides the few surviving photos of individuals who had done this, there are contemporaneous reports of tattoo artists seeing a significant increase in business after the passage of the social security act.

In newspaper archives, we can find references to this practice fairly frequently in the 1937-1940 time period, including headlines like "social security law boon to tattoo artists" and some fun ones like "victim is identified by social security tattoo."

Of course I'm sure the practice was relatively fringe, but newspaper archives show us that it was not, on the other hand, especially isolated. Newspapers report on the practice occurring locally in nearly every state (that existed at the time).

I also think you somewhat underestimate the popularity of tattoos at the time. While they were regarded as fringe and somewhat antisocial, they were widely available and particularly popular in some circles, as they are today.

I think young people don't really understand how quickly (and recently) tattoos went from something really fringe to something fairly socially acceptable. I remember cops occasionally harassing my (white) dad because he had a few forearm tattoos back in the early to mid 90s.

I concur, have never heard of this practice. It was extremely rare for anyone to have tattoos even sixty years ago.

SSNs were definitely less protected -- I remember mine showing up on my student ID in the 80s, on school rosters in the Navy in the 90s, etc. But tattoos? No.