As per my understanding there is no direct way to get the choices from choice field in alphabetical order using SharePoint REST API (correct me If I am wrong).
var fruits = ["Banana", "Orange", "Apple", "Mango"];
You could take the following steps:
Initialize 2 variables, one type is array and one type is string.
Use rest api to get the choice field.
Parse the JSON "Body", you would get the current choices as array "results"
Set the array variable to "results", then append one value to the array varibale.
Set the string varibale to the arrary variable.
Update the ...