It's a "secret language"

The rules divide languages into three groups: Standard, Exotic, and Secret. In the section on Languages about what you can pick as a language, the rules say:

Choose your languages from the Standard Languages table, or choose one that is common in your campaign. 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.

That describes thieves' cant as a "secret language", which (if the DM approves doing so) you could take like any other language given by your background, or learn like researching any other language.

It's a "secret language"

The rules divide languages into three groups: Standard, Exotic, and Secret. In the section on Languages about what you can pick as a language, the rules say:

Choose your languages from the Standard Languages table, or choose one that is common in your campaign. 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.

That describes thieves' cant as a "secret language", which (if the DM approves doing so) you could take like any other language given by your background, or learn like researching any other language.

I could certainly understand a DM not approving doing so, given how different thieves' cant is from other languages. But you're specifically asking about how the rules handle it mechanically, and from that Languages section I think it's pretty clear that from a rules perspective it's a language like any other.

It's a "secret language"

The rules divide languages into three groups: Standard, Exotic, and Secret. In the section on Languages about what you can pick as a language, the rules say:

Choose your languages from the Standard Languages table, or choose one that is common in your campaign. 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.

That describes thieves' cant as a "secret language", which you could take like any other language given by your background if the DM approves.

It's a "secret language"

The rules divide languages into three groups: Standard, Exotic, and Secret. In the section on Languages about what you can pick as a language, the rules say:

Choose your languages from the Standard Languages table, or choose one that is common in your campaign. 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.

That describes thieves' cant as a "secret language", which (if the DM approves doing so) you could take like any other language given by your background, or learn like researching any other language.