The Dutchman, who captained the Gunners, netted a brace to help see off Coca-Cola Championship outfit Plymouth 3-1 at the Emirates Stadium and set up a tricky fourth round trip to Cardiff.
Van Persie, signed from Feyenoord in August 2004, was at t
he end of his first campaign with the Gunners when they beat Manchester United on penalties to win the FA Cup at the Millennium Stadium in the Welsh capital.
Now the world's oldest knockout competition is back at its traditional home, the 25-year-old is hoping for a repeat performance under the Wembley arch in May.
"For me it is a big thing because the FA Cup has a big history going back a hundred years. I was lucky enough to win it in my first year and I hope to win it this year as well," he said.
"I know it is going to be difficult because you can draw teams that give absolutely everything.
"There are big tests coming up but hopefully we can go far and make at least the final."
Van Persie added: "When we were in the final last time, we were playing at Cardiff. It was fantastic in front of 70,000 people, but it is still a dream for me to play at Wembley. I have never played there."
Cardiff are currently fourth in the Championship and are chasing a place in the Premier League.
Elsewhere in the draw, north London rivals Tottenham were drawn away to Southampton or Manchester United and Liverpool entertain Everton.
Chelsea host Ipswich if they beat Southend in their replay.
Nottingham Forest's reward for beating Manchester City yesterday is a trip to bitter rivals Derby while Coca-Cola League One Hartlepool, who beat Premier League Stoke, host West Ham.
Torquay, the other non-league side left in the draw, were also drawn at home with Coventry the visitors.
DrawLiverpool v Everton
Southampton/Man Utd v Tottenham
Hull/Newcastle v Millwall/Crewe
Sunderland v Blyth/Blackburn
Hartlepool v West Ham
Leyton Orient/Sheff Utd v Charlton/Norwich
Cardiff v Arsenal
Portsmouth/Bristol City v Histon/Swansea
Chelsea/Southend v Ipswich
Cheltenham/Doncaster v Aston Villa
West Brom/Peterborough v QPR/Burnley
Torquay v Coventry
Kettering Town v Fulham
Watford v Leicester/Crystal Palace
Derby County v Nottingham Forest
Birmingham City/Wolves v Middlesbrough
