Palace reportedly spent a club-record fee of £7 million to sign McArthur from Wigan Athletic on a busy Monday that also saw Kevin Doyle and Zeki Fryers join Warnock's side.
Warnock, tasked with continuing the good work done by ex-manager Tony Pulis last term, saw his side claim a 3-3 draw at Newcastle United last weekend in the first match of his second spell at the club.
The result gave Palace their first Premier League point of the season and Warnock is confident his men can kick on after expressing delight regarding his deadline-day business.
"We worked hard all day and managed to get three lads in," Warnock told the Croydon Advertiser.
"James McArthur - I've been after him for a while, he's a super player.
"I remember watching him up in Scotland [when at Hamilton Academical] and kept in touch with his progress.
"I think he's got a lot to prove as well. He's back with the Scotland squad and he's looking forward to starting. He's just our kind of player."
Palace's next Premier League test sees them host the only side below them - Burnley - on September 13.
