Embark on this celestial journey with me, my dears. Let the stars be your guide as you navigate the coming year with cosmic confidence and a touch of astrological magic.

JavaScript (Node.js),  64  62 bytes

Expects (month)(day).

This version builds the UTF-8 encoding of the code point (from 0xE2 0x99 0x88 for Aries to 0xE2 0x99 0x93 for Pisces).

m=>d=>Buffer([226,153,136+(m+=9^d<24+~"1342321"[m%12])%12])+''

Try it online!

ES6, 63 bytes

Using the more straightforward String.fromCharCode() with a direct code point is one byte longer.

m=>d=>String.fromCharCode(9800+(m+=9^d<24+~"1342321"[m%12])%12)

Try it online!

Charcoal, 31 bytes

Ｎθ℅⁺⁹⁸⁰⁰﹪⁺⁸⁺θ›Ｎ⁺¹⁸Ｉ§”)⊞⌊4\`ζ”θ¹²

Try it online! Link is to verbose version of code. Takes separate month and day as inputs. Explanation:

Ｎθ                           First input as a number
              Ｎ              Second input as a number
             ›               Is greater than
                    ”...”    Compressed string `310212344444`
                   §         Cyclically indexed by
                         θ   Input month
                  Ｉ          Cast to integer
               ⁺             Plus
                ¹⁸           Literal integer `18`
           ⁺                 Plus
            θ                Input month
         ⁺                   Plus
          ⁸                  Literal integer `8`
        ﹪                    Modulo
                          ¹² Literal integer `12`
   ⁺                         Plus
    ⁹⁸⁰⁰                     Literal integer `9800`
  ℅                          Convert to Unicode
                             Implicitly print

Retina 0.8.2, 112 bytes

T`d`k-m`1.-
T`d`l`.-
T`b-m`c-mb`.-3|[bce]-2|[df]-2[1-9]|[gm]-2[2-9]|[h-l]-2[3-9]|c-19
.(.).+
$1
T`e-mb-d`♈-♓

Try it online! Link includes test cases. Takes input in the format mm-dd. Does not output a Unicode variation selector, but the output looks fine in TIO to me. Explanation:

T`d`k-m`1.-

Change October to December to k to m, which will become Scorpio to Capricorn.

T`d`l`.-

Change January to September to b to j, which will become Aquarius to Libra.

T`b-m`c-mb`.-3|[bce]-2|[df]-2[1-9]|[gm]-2[2-9]|[h-l]-2[3-9]|c-19

Increment the encoded sign if the day is past the cutoff date for the next sign.

.(.).+
$1

Delete everything except the encoded sign.

T`e-mb-d`♈-♓

Decode to a Unicode Zodiac sign.

Jelly, 27 bytes

“£f{ẋ’b5⁸ị+19>_@⁸_3%12+⁽#1Ọ

A dyadic Link accepting an integer, month, on the left and an integer, day, on the right that yields a character.

Try it online! Or see a whole year.

How?

“£f{ẋ’b5⁸ị+19>_@⁸_3%12+⁽#1Ọ - Link: M; D
“£f{ẋ’                      - 53343748
      b5                    - to base five -> [1, 0, 2, 1, 2, 3, 4, 4, 4, 4, 4, 3]
        ⁸ị                  - get the item at 1-indexed index M
          +19               - add nineteen to it
             >              - is that greater than D? -> 1 or 0
              _@⁸           - subtract from M -> M-1 or M
                 _3         - subtract three (offset since characters start at March)
                   %12      - modulo twelve
                       ⁽#1  - 9800
                      +     - add
                          Ọ - cast to character