A few, but they all explicitly require DM's permission
As it is a method of communication, can it be taken as a language?
Nope. As a game term, Thieves' Cant is a class feature, not a language (more precisely, it is a "secret language", thanks @Peter Cooper Jr. for the catch; see his answer for more info).
is it mechanically equivalent to something
Nope. Thieves' Cant is a unique class feature. Even spells like Comprehend Languages do not allow you to understand Thieves' Cant.
Are there any other rule mechanics e.g. background, that could grant Thieves' Cant?
Nope. There are no "official" ways to get this feature other than taking a level in Rogue. However, with the DM's approval, custom backgrounds or homebrewed class archetypes can give Thieves' Cant.
You can have it from a custom background feature
Lore-wise, Thieves' Cant is a skill to hide secret messages in whatever language you are currently speaking. Such a skill can be learned.
Rules as written, a DM can allow Thieves' Cant as a custom background feature. See the PHB page 125 "Customizing a background":
If you can't find a feature that matches your desired background, work with your DM to create one
You can also choose it as a language with the DM's permission
There is explicit mention of thieves’ cant in the Languages section of the rules:
With your DM’s permission, you can instead choose a language from the Exotic Languages table or a secret language, such as thieves’ cant