The London-based rights organisation said today police officers guilty of such alleged abuses often escaped punishment.
Efforts to combat the problem were weak outside the capital, Tbilisi.
"Impunity for torture and ill treatment is a big problem. In dozens of cases where the procuracy has opened investigations, the perpetrators have not been brought to justice," said Amnesty's researcher on Georgia, Anna Sunder-Plassmann.
Among methods used to torture or ill treat detainees were electric shocks, putting plastic bags over the detainee's head, cigarette and candle burns, placing the barrel of a gun in someone's mouth and threatening to shoot them and beating with objects including truncheons and guns, Amnesty said.
The rights group urged President Mikhail Saakashvili to set up an independent body to review all investigations into allegations of torture and ill-treatment, which would have the powers to issue a public report.
It also called for law enforcement authorities in the former Soviet republic to examine all allegations promptly in an impartial manner and to prohibit the use of masks as a means of disguising officers' identities, except to protect their personal protection.
"The government should keep the eradication of torture and ill treatment on its agenda as a priority issue. While important steps have been taken, the government still has a long way to go. A long term approach is needed to achieve lasting results," Ms Plassmann said.