In 1702, he was at Epsom when Prince George of Denmark, husband of Queen Anne fell ill. According to tradition, Arbuthnot treated the prince successfully. According to tradition again, this treatment earned him an invitation to court. Also around 1702, he married Margaret, whose maiden name is possibly Wemyss. Although there are no baptismal records, it seems that his first son, George (named in honour of the prince), was born in 1703. He was elected to be a Fellow of the Royal Society in 1704. Also thanks to the Queen's presence, he was made an MD at Cambridge University on 16 April 1705.