The 'Love Story' hitmaker began dating Robert F Kennedy Jr's son last month after spending the US Independence Day holiday at the Kennedy family compound in Massachusetts, reported Daily Star.
"She returned to Hyannis Port again at the end of July, but last week it was 18-year-old Kennedy's turn to meet the parents as he travelled to Swift's home in Nashville to get to know her mum Andrea and dad Scott," a source said.
Swift, 22, previously dated Joe Jonas, Taylor Lautner and Jake Gyllenhaal.