Tarsicia is the feminine of Tarsicius — "of Tarsus." Saint Tarsicia of Rodes (7th c.) was the Visigothic-Spanish princess (granddaughter of King Wamba) who fled the court to live as a hermit in the Galician forests — patron saint of Asturias and Galicia.
Distinct from the male Roman martyr Saint Tarsicius.
Tarsicia 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 Tarsicia reduce to 8, The Visionary. This is a traditional interpretive system, not a factual claim about the name.