Aisha Ali-Khan, 33, admitted the charge at London's Southwark Crown Court.
Her husband, former detective inspector Mohammed Afiz Khan, 46, was head of the Muslim contact unit at the Metropolitan Police's counter-terrorism unit SO15, but has since been dismissed.
He has already pleaded guilty to two misconduct charges.
The pair will be sentenced together on July 11.
Ali-Khan admitted that on or about August 24 2012, she encouraged Khan to obtain personal data relating to people she believed had sent emails.
She previously pleaded not guilty to a second charge of encouraging misconduct in a public office.
Khan was originally charged with two counts of misconduct in a public office and four counts of data protection offences between May and September 2012.
In December, he pleaded guilty to a charge of misconduct in that he disclosed restricted information he had obtained relating to the arrest of radical Muslim cleric Anjem Choudary to Ali-Khan while she was employed by Mr Galloway on or around May 22 2012.
He also admitted a charge of misconduct relating to obtaining CCTV from South Yorkshire Police between March 16 and April 30 2012.
Khan pleaded not guilty to two data protection charges but did not enter pleas to the other two.
The pair, of Keighley, West Yorkshire, were both given bail.