I need to make it display rich text like this:
"You got 🍎 Apple!"
where the "🍎" is a custom texture called apple.png in my project folder.
I tried using the [img] tag but it makes the text and apple icon misaligned.

Try using the table and cell tags.
This example assumes that the path for the image is res://apple.png:

[table=3]

[cell]You got[/cell]
[cell][img]res://apple.png[/img][/cell]
[cell]Apple![/cell]

[/table]

https://docs.godotengine.org/en/4.4/tutorials/ui/bbcode_in_richtextlabel.html#reference

    DaveTheCoder
    no luck. it results in the same thing although now it misaligns the words as well.

      Try adjusting the dimensions of the image to match the text. You can specify the image width and height using BBCode in Godot 3:
      https://docs.godotengine.org/en/3.6/tutorials/ui/bbcode_in_richtextlabel.html#reference

      Godot 4 has enhancements to BBCode that appear to do exactly what you want:
      https://docs.godotengine.org/en/4.4/tutorials/ui/bbcode_in_richtextlabel.html#image-and-table-vertical-alignment

      Alternatively, you could create an image outside of Godot that contains the text and the apple, and then display that image in Godot.