In his historical study Derek Walters has traced the introduction of the Animal Zodiac into Chinese astrology in the period from the 1st to 6th century AD, being introduced from Northwestern China. However, dozens of animals were assigned (and still are) to things like Lunar Mansions, or the 4 great divisions of the sky, and other categories of what we would refer to as various Chinese "astrological" calculations and categories.
The "original" calculating method (regarding indications of celestial/macrocosmic trends and influences) was the 10 celestial stems/12 earthly branches method* which has been dated by scholars to between 2 and 3,000 BC: each stem and branch had a symbol (original Chinese character) to depict it, but these were not the later "Animal Zodiac" with which stem and branch computation eventually became united in the early centuries of the Current Era...
*I have always been intrigued by these numbers-12, 10, regarding stem/branch celestial calculations; because they did not arise in any connection whatsoever with Western astrology (or cosmology), yet the 12 branches cause me to wonder about the 12 signs (of the Western, and the later Chinese Animal, zodiacs) and the 10 stems cause me to wonder about the 10 planets of our solar system (Sun, Moon, other traditional 5 planets, and the 3 outers)...but I have not come to any conclusions (even anywhere close to any) in my speculations regarding the stems and branches...