An emotional Rankine returned to Australia on Tuesday night and fought back tears during a public apology at Adelaide Airport.
"Going away has given me space to reflect and educate myself to understand the weight of my mistake," Rankine told reporters.
"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."
The 25-year-old is the sixth AFL-listed player in 16 months to be banned for an on-field homophobic slur.
Rankine has served one game of his four-match suspension.
His only hope of playing again this season is if his Crows lose Thursday night's qualifying final against Collingwood but then progress to the grand final when he would be available.
Rankine said he was "in no way a victim" and expressed remorse for his homophobic slur directed at a Collingwood player in an August 16 game.
"There was no excuse. It was wrong and I take full responsibility," he said.
"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's public comments came after arriving on a flight from Doha. He had spent time in Italy to avoid the spotlight in Adelaide in the wake of his suspension.
When the AFL announced Rankine's ban on August 21, Crows chief executive Tim Silvers said he was nervous about the mental health of the star utility.
Rankine is not expected to attend Adelaide's last training session on Wednesday morning ahead of the qualifying final against the Magpies at Adelaide Oval.
Rankine was banned after a protracted AFL investigation into his offensive comment.
The day after the August 16 fixture, Rankine privately apologised to the Collingwood player.
That apology came as the AFL's integrity unit launched an investigation.
The AFL initially decided on a five-game ban.
But the penalty was reduced to four matches due to "compelling medical submissions", the league's chief executive Andrew Dillon said when announcing the suspension on August 21.
Dillon and the Crows have refused to detail the nature of the submissions.
Since last April, Rankine, Port Adelaide's Jeremy Finlayson (three games), Gold Coast's Wil Powell (five games), West Coast's Jack Graham (four games) and two AFL-listed players in the VFL - Sydney's Riak Andrew (five games) and St Kilda's Lance Collard (six matches) - have been suspended for on-field homophobic comments.
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