If your file will only ever be a single line you can use:
IFS=$' \t' read -ara array < file.txt If it can have multiple lines one way to do it would be to first transform the file so that every word has it's own line and then use bash's readarray (only available in bash 4.0 or later which might be an issue for you if you are on macos):
readarray -t array < <(tr -s '[:space:]' '\n' < file.txt)