Rankine, 22, posted a screenshot of the message on his Instagram account on Monday night, showing he'd received the disgusting abuse during the win.
"Pretty disappointing to STILL have to deal with this. When will it end," Rankine wrote on his Instagram.
He was in great touch in the Crows' 39-point win against Fremantle on Saturday, kicking three goals.
The AFL's integrity department has been contacted and will investigate the incident with the hope of identifying the individual involved.
The incident comes just weeks after Western Bulldogs young gun Jamarra Ugle-Hagan was racially abused by a fan when his side played St Kilda.
Adelaide CEO Tim Silvers labelled the "deliberate" attack on Rankine as "totally unacceptable and disgraceful" and said the club would support the player and his family.
"All of us have a responsibility to call out this type of reprehensible behaviour," he said.
"Equally, we must also take the time to understand the hurt it causes the person who has been targeted, as well as in this instance all Aboriginal and Torres Strait Islander people.
"From the Chairman and Board of Directors through to our players, coaches, staff and volunteers, we are determined to use our voice and platform to continue to make a stand.
"We are committed to playing a role in educating as many people as we possibly can."
The AFL echoed the Crows' sentiments, declaring "there is no place in our game for anyone who vilifies our players".
"We stand with the club in calling out the racist comments, comments that cause significant hurt and harm for Aboriginal and Torres Strait Islander peoples," the AFL's statement read.
"We strongly support all our Aboriginal and Torres Strait Islander players and condemn the racial vilification of anyone in the community in football.
"The AFL continues its ongoing implementation of the 'Peek rule' and the work never stops against vilification, especially in the online space and the challenges surrounding the identification of antagonists."
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