The England forward held top spot before moving to Lyon and is desperate to reclaim it from new team-mate Vivianne Miedema.
The England forward, 27, was the WSL’s record scorer with 49 goals when joining Lyon from Manchester City two years ago.
Parris has since been overtaken by new Arsenal team-mate Vivianne Miedema (60) and City striker Ellen White (54).
Liverpool-born Parris said: “That’s obviously at the top of my mind, let’s be honest. I’m a striker, I want to score goals and I want to make history.
“In every team that I’m in I want to leave a mark and if I can leave a mark at Arsenal and the WSL at the same time, let’s go for it.”
Parris scored 33 goals in 53 appearances in two seasons for Lyon and won the 2019-20 Champions League as part of a treble.
Lyon confirmed the deal to seal Parris’ WSL return had cost Arsenal 80,000 euros (£69,000), which could increase to 100,000 euros (£86,000).
Parris said she had specifically requested the number 14 shirt at her new club, made famous by Arsenal great Thierry Henry.
“Fourteen speaks for itself. Thierry Henry,” Parris said. “When I was growing up he was my role model and he obviously wore the Arsenal badge.
“I had the pleasure of being interviewed by him and being able to speak to him about Arsenal and football. It’s crazy the similarities, how our thought processes align.
“The way we think going into football games. We demand so much from ourselves. People say it’s pressure from the outside that makes you want to improve. It’s not, it’s pressure from within.
“Your expectation level of yourself and also he spoke about his dad and how he was a big influence on him and he never wanted to disappoint his dad.
“That’s how I feel with my dad. Every time I come off the pitch he’s the first person I go to because I know he’s going to give me something real and tell me how it is, 100 per cent he’s not going to hold back.”
Parris said she was excited at the prospect of linking up with Netherlands forward Miedema, whose 60 goals have come in 67 appearances for the Gunners.
“You want to play with the best talent and in Vivianne you have that,” Parris added. “She scores goals for fun.
“She doesn’t just score goals though, she brings others into play and that’s what she likes doing. She’s been very clear about that.
“I want to play for Arsenal because I want to push the team forward so they can win trophies again because Arsenal have a great history and you need big players to do that.”
Parris has scored 14 goals in 52 appearances for England and is currently part of the Great Britain squad for this summer’s Tokyo Olympics.
She was the 2019 FWA Women’s Footballer of the Year and helped City win the 2016 WSL, two FA Cups and two League Cups.
Arsenal finished third in the WSL last season to secure a return to the Champions League.