Priority Moments flags up offers for O2's 22 million customers from nearby retailers participating in the scheme, including WH Smith and French Connection.
The app has become popular even before the 26 July launch of a £6m ad campaign for the programme, which launched last week.
Last week's number one, the official app for golf's Open Championship, which ended on Sunday, is down to number five.
ITV Player holds on to the second spot, while Facebook climbs one place to number three.
The Sun's Dream Team fantasy football game is a new entry at number four and Channel 4 News debuts at number six.
Next and the Harry Potter Spells app, further down the list, are re-entries.
Unusually, there are no Sky apps in this week's chart.
The chart is powered by analytics app developed by with non-commercial branded apps removed.