Rankine arrived in Adelaide on Tuesday night after being sent to Italy at the behest of his club to avoid the spotlight in the aftermath of his four-game suspension.
Speaking at Adelaide Airport, the Crows ace said he was sorry for the hurt caused by his homophobic remark to a Collingwood player in an August 16 game at Adelaide Oval.
"I want to start by saying how deeply sorry I am for what I said," Rankine told reporters.
"There was no excuse, it was wrong and I take full responsibility.
"I'm disappointed in myself and I know I have let a lot of people down.
"I want to apologise to anyone who I have hurt and offended.
"I understand that word was offensive, harmful, it's hurtful and has no place in our game or our society."
Rankine has served one match of his four-game ban.
The suspension offers him hope of playing in the grand final, should the Crows reach the premiership decider.
But Rankine will only be available if Adelaide lose a home qualifying final against Collingwood on Thursday night and then advance to the grand final.
The 25-year-old said he was "in no way a victim".
"But going away has given me space to reflect and educate myself to understand the weight of my mistake," he said.
"And I am fully committed to bettering myself.
"In the next few days I will be standing in front of my teammates and the AFLW and apologising to them personally - and they deserve this at the very least.
"From here, all I can do is put my head down, work hard, support my teammates in the best way I can and show through my actions that I am going to learn from my mistake.
"More than anything, I want this club to succeed so I will be doing everything I can to gain everyone's trust back and have a positive impact impact on society and my supporters."
An emotional Rankine ended with media conference with a "thank you" and didn't answer questions.
The AFL initially decided on a five-game ban for the forward who is renowned as among the most talented players in the competition.
But that penalty was reduced to four matches, with AFL chief executive Andrew Dillon cited "compelling medical submissions" made by the Crows on Rankine's behalf.
Dillon and Adelaide hierarchy have refused to detail the nature of the submissions.
But Crows chief executive Tim Silvers, when the ban was announced on August 21 after a four-day AFL investigation, expressed nervousness for Rankine's mental health.
Rankine was the sixth AFL-listed player banned for an on-field homophobic comment in the past 16 months.
In July, West Coast's Jack Graham was banned four games for  for an homophobic remark to a GWS player.
In April last year, Port Adelaide's Jeremy Finlayson was suspended for three games and, the following month, Gold Coast's Wil Powell was suspended five matches, both for making homophobic slurs to opponents.
Two VFL players - Sydney's Riak Andrew (five games) and St Kilda's Lance Collard (six matches) have also recently been banned for on-field homophobic comments.
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