AskEraser allows users to immediately delete search queries stored on Ask's servers, in contrast to rivals such as Google which stores data for 18 months.
How personal data is used is becoming more of an issue as people live more of their lives via search engines.
Some are concerned about possible deals between search engines and ad firms.
In America consumer advocacy groups have expressed doubts about a proposed merger between Google and ad-serving company DoubleClick, which is currently being reviewed by US regulators.
Jumping on the privacy bandwagon, Ask is offering users the chance to take charge of what happens with their search history.
An AskEraser link will feature prominently on the Ask.com homepage and, when enabled by the user, will delete all future search queries and associated cookie information from its servers.
The information it destroys includes IP address, user ID and session ID along with the complete text of a query.
"For people who worry about their online privacy, AskEraser now gives them control of their search information," said Jim Lanzone, chief executive of Ask.com.
But some critics have pointed out that it doesn't entirely erase all information, as search queries relating to advertisements supplied by Google will continue to be passed to the search rival.
Other search engines are attempting to quell concerns about privacy and most operate polices which mean search histories are deleted between a year and 18 months after they were made.
But some consumers are getting twitchy about how their data is shared, following some high-profile cases.
In August 2006 AOL was forced to apologise after it released the search queries of more than 650,000 of its US subscribers to help in academic research.
Although users' names were not associated with the search terms, fears were raised that the queries contained personally identifiable data. It was not clear which researchers were given the data and how they intended to use it.
And just last week Mark Zuckerberg, the founder of social networking site Facebook, had to make changes to a new advertising system after more than 50,000 users complained about it.
Called Beacon, the system is designed to track web shopping on partner sites outside Facebook with the intention of providing targeted adverts to the social network based on purchases.
After complaints the site was invading privacy, Facebook changed Beacon from an opt-out system to opt in.
Mr Zuckerberg has said users can now switch off Beacon completely.
'Paying with privacy'
Despite these cases not everyone is convinced that privacy is a big enough winner for users to desert their favoured search engine for Ask.
"The press loves to run stories about the hidden privacy concerns caused by data collected online, but consumers have taken an 'out of sight, out of mind' approach," commented technology blog TechCrunch.
"We're finding that people are willing to pay for the best free products with their privacy," it added.
Surveys conducted in the US seem to bear this out. While a majority of Americans say they are concerned about their online privacy, only a tiny percentage are actually prepared to take steps to protect it.
"Search log data is anonymised within 13 months of collection except where users request otherwise or where Yahoo! is required to retain the information to comply with legal obligations.," the firm said in a statement.
"We believe the 13 month-policy is the appropriate timeline to honour our commitment to our users' privacy while preserving our ability to defend against fraudulent activity and continue to improve our services," it read.
Google said it had no plans to implement such a tool.
The highly competitive search engine market, which is dominated by Google, means rivals are increasingly searching for applications that differentiate them.According to internet measurement firm comScore, Ask accounted for 4.7% of US searches during October. Google took the lion's share with 58.5%, with Yahoo accounting for 22.9% and Microsoft for 9.7%.