A rolled copper or copper alloy foil having a roughened surface formed of fine copper particles is obtained by subjecting a rolled foil to roughening plating with a plating bath containing copper sulfate (Cu equivalent of 1 to 50 g/L), 1 to 150 g/L of sulfuric acid, and one or more additives selected among sodium octyl sulfate, sodium decyl sulfate, and sodium dodecyl sulfate under the conditions of temperature of 20 to 50° C. and current density of 10 to 100 A/dm2. The foil has reduced craters, which are defects unique to rolled foils having a roughened surface, has high strength, adhesive strength with the resin layer, acid resistance and anti-tin plating solution properties, high peel strength, favorable etching properties and gloss level, and is suitable for producing a flexible printed wiring board capable of bearing a fine wiring pattern. A method of roughening the rolled foil is also provided.