To me, as an American, the word "rather" already feels both old-fashioned and British, but "rather a" feels MORE old-fashioned and MORE British than "a rather." As an American, I'd usually use words like slightly, somewhat, fairly, or kind of.
Google Ngrams shows the begfore 1905 in America, and before 1930 in England, "rather a" was more common than "a rather". Now, i both countries, "a rather" is much more common than "rather a".
But, as everyone else said, the difference is very small.