I was born on June 27th of the lunar calendar, so what sign am I?

Constellations are calculated according to the solar calendar;

Constellation name, date, constellation attributes

Aries: fire sign

Taurus 04/20- 0520 Earth Sign

Gemini: air signs

Cancer: water sign

Leo fire sign 07/23-08/22

Virgo: Earth sign

Libra: air signs

Scorpio10/23-11/21water sign

Sagittarius11/22-12/21fire sign

Capricorn12/22-0119 earth sign.

Aquarius: air signs

Pisces: water sign