The decision has prompted widespread anger with the RSPCA calling for a review of indigenous hunting activities.

Video of the incident in South Australia earlier this year caused outrage as it showed the off-duty senior community constable, identified in media reports as Waylon Johncock, following a wombat along a dirt road while throwing rocks at it as he is cheered on by a friend in a car.

SA Police conducted an internal investigation and have taken advice from the Director of Public Prosecutions which said as an Aboriginal man, the officer had the appropriate permit to hunt wombats for food.

"Whilst distressing to many who viewed the video, it has been established the senior community constable's actions were not inconsistent with traditional hunting practices," Police Commissioner Grant Stevens said in a statement on Friday.

"I have been advised that the wombat in the video was killed and eaten."

The incident occurred in the Gawler Ranges, east of Ceduna.

After being uploaded to the internet it prompted widespread anger with calls for police to take action.

Police said they received an unprecedented number of phone messages, emails and social media comments demanding a response.

Mr Stevens said he found the video both confronting and disturbing.

"I take personal displeasure in seeing any animal distressed, or being killed as the wombat was killed," he said.

"I know many shared in my shock and dismay."

But legal advice from the DPP had established that if charges were laid, there would be no reasonable prospects of conviction.

In respect to the internal investigation, the officer has been given counselling and provided with managerial advice.

"It is clear from the outpouring of emotions that some may question the outcome of this investigation," Mr Stevens said.

"I can reassure everyone that the most thorough of investigations has been undertaken in this matter.

"The senior community constable is well regarded and respected by his colleagues, peers, supervisors, managers and the local community in which he serves.

"I have confidence in his abilities to perform his current role as a community constable."

The RSPCA South Australia said if wild animals were legitimately hunted for subsistence, that must be conducted humanely.

"Controls exist in Australia to avoid unnecessary suffering being inflicted on animals in almost any situation where humans interact with animals, and we see no justification for any exceptions to this protection," it said in a statement.

"RSPCA South Australia respects the indigenous culture and the connection indigenous communities have with Australian wildlife.

"There are, however, countless examples in many different cultures around the world, where traditional cultural practices are no longer acceptable and have ceased or are subject to various controls."

When the video first surfaced the Wombat Awareness Organisation launched a petition, that has since attracted more than 350,000 signatures, also seeking a review of SA's traditional hunting laws.

Australian Associated Press