Launched on 22 May, the Argos app allows people to check prices and stock by store location, as well as browse the retailer's product database.
Sandwich chain Subway's loyalty-based app Subcard also grew in popularity this week, rising four places to number three.
Further testimony to the appeal of retail apps comes from the presence of eBay, Amazon and Tesco in the chart.
Media players Sky and Google continue to occupy many of the other slots, but are joined this week by the London Evening Standard's recently updated app.
The chart is powered by analytics app developed by with non-commercial branded apps removed.