A few, but they all explicitly require DM's permission
-
> As it is a method of communication, can it be taken as a language?

Not as a part of standart character generation. You will require an [explicit DM's permission][5]:

> *With your DM's permission, you can instead choose a language from the Exotic Languages table or a secret language, such as thieves’ cant or the tongue of druids.*

Thieves' Cant is a [unique][1] class feature. Even spells like [Comprehend Languages][2] do not allow you to [understand Thieves' Cant][3].

> Are there any other rule mechanics e.g. background, that could grant Thieves' Cant?

There are no "official" standard ways to get this feature other than taking a level in Rogue. With the DM's approval, custom backgrounds or homebrewed class archetypes can give Thieves' Cant.  

Lore-wise, Thieves' Cant is [anti-language or secret language][4] is the jargon or language of a group, often employed to exclude or mislead people outside the group. It is a skill to hide secret messages in whatever language you are currently speaking.

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*


  [1]: https://rpg.stackexchange.com/questions/53898/
  [2]: https://www.dndbeyond.com/spells/comprehend-languages
  [3]: https://rpg.stackexchange.com/questions/115608/
  [4]: https://en.wikipedia.org/wiki/Cant_(language)
  [5]: https://www.dndbeyond.com/sources/basic-rules/personality-and-background#Languages