Concluding an investigation triggered by Sale, it found Arscott's behaviour had been "inappropriate" and gave him a written warning.
The RFU said the player had discussed tactical information about his side's defence with his brother on the night before a Jan. 1 match that Sale lost 24-23.
"The RFU has determined that this information, while at the lower end of the scale of seriousness, falls within the definition of inside information," it said.
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Sale terminated Tom Arscott's contract on Jan. 20 after their own disciplinary investigation and hearing.
The RFU, who interviewed 25 individuals from both clubs, found no evidence of betting or fixing and also no evidence that Bristol had changed their strategy to deal with Sale's positional changes.
RFU disciplinary head Gerard McEvilly said Arscott's sacking by Sale had been taken into account in determining his punishment.
"These issues have arisen because of the inappropriate sharing of information while players were socialising in the same hotel before the match," he said.
"Therefore, the RFU is strongly recommending to both clubs that all their players are reminded of their contractual and ethical obligations to their employing clubs and of the problems that may arise should confidential/inside information be passed between individuals."
South Africa secure second Test 27-9 victory over the Lions at Cape Town Stadium