Anca is the Romanian short form of Ana (Anna) — meaning "grace." Anca Damian (born 1962) is the Romanian filmmaker; Anca Heltne (born 1984) is the Romanian shot putter.
Anca is widely used in Romania.
Anca does not currently appear in the US Social Security Administration's top 1,000 girls' names, so we don't publish a US rank or birth count for it. That says nothing about the name's standing elsewhere in the world — only that it sits outside the ranked US data we rely on.
In Pythagorean numerology the letters of Anca reduce to 1, The Leader. This is a traditional interpretive system, not a factual claim about the name.