The comeback comes a month after the iPhone maker said it would allow the application with updates aimed at curbing incitements to violence.
Parler said in a statement that it provided "incontrovertible evidence to Congress and the public that... (its) scapegoating and deplatforming was profoundly unjust."
The company claimed to have more than 20 million users before Apple and Google marketplaces pulled the plug and the app was effectively shut down when Amazon Web Services cut ties over allegations the platform failed to stop incitement of violence by Donald Trump's supporters ahead of the January 6 riots at the US Capitol.
Separately, Parler announced the promotion of George Farmer to chief executive from chief operating officer, as part of a leadership shakeup at the company.
"Parler began as a small, start-up company that differed from its Big Tech competitors in its commitment to the free market of ideas in the full spirit of the First Amendment," Farmer was quoted as saying by AFP.
"For the past two months I have worked with an incredible team of people, under the leadership of (interim CEO) Mark Meckler, to bring Parler back online and return to Apple's App Store after we had been unfairly maligned by the media and its allies in Big Tech and Congress," he added.
According to a report by the Washington Post, the new version of Parler on Apple devices will be moderated with artificial intelligence to filter out hateful content, but that these comments could still be viewed on the web or other devices.
Parler, which calls itself "the free speech social network," did not confirm the report by the Post, which said that posts labeled as hate speech or with racial slurs could be viewed by clicking though on non-Apple devices.