Tamil Sign Anusvara

No. The ring is a pulli form, not this separate anusvara.

Unicode 18.0 says ஂ is not used in Tamil. Tamil pulli ் may appear as a dot or hollow ring, depending on the font. Two 2012 proposals to Unicode’s character standard disagree over whether ஂ appears in Tamil-script Sanskrit and Buddhist transcriptions: one shows that use, while another says it is unattested. Keep this sign only where your edition uses it.

The name recalls anusvara in Brahmi, an early South Asian script: there it marked a nasalized vowel or a nasal sound before a following stop. Brahmi is attested by the third century BCE and was used to write Tamil from the second century BCE. Old Tamil Brahmi also used a dot-like pulli to show that a consonant had no built-in vowel.

When should I type this Tamil mark?

Only when the source edition uses it.

Tamil keyboard references document Tamil99 and Typewriter Unicode layouts. CLDR 43 lists ஂ among Tamil characters without a keyboard mapping, so if your chosen layout has no key for it, use your system’s Unicode character picker.