That's a good example of the need to translate whole sentences, not single words. If you pick "turn into", you're going to have to do some fancy footwork to keep it from sounding bad.

"It was rather easier to for a free man to turn into a slave" - Sounds wrong, because when somebody is enslaved, for whatever reason, one doesn't usually think of him as "turning into" a slave - like Daphne turning into a laurel tree in Ovid's Metamorphoses. Well, I know that's what превратиться means, but still - to me, "turn into" sounds odd in English.

So, you'd have to change it in some way, maybe; "It was rather easier to turn from being a free man, into a slave."

Still sounds lousy, to my ear. And that's because "turn into" really isn't the best way to express a shift from the status of a free man, to slavery. Other options:

It was rather easier to go from being a free man, into slavery.

It was rather easier for a free man to become a slave. (Much better!)

It was rather easier for a free man to become enslaved. (Context permitting.)

It was rather easier for a free man to find himself in slavery.

Etc. etc.