Ongoing searches for exoplanetary systems have revealed a wealth of planets with diverse physical properties. Planets even smaller than the Earth have already been detected and the efforts of future missions are aimed at the discovery, and perhaps characterization, of small rocky exoplanets within the habitable zone of their stars. Clearly, what we know about our planet will be our guideline for the characterization of such planets. But the Earth has been inhabited for at least 3.8 Gyr and its appearance has changed with time. Here, we have studied the Earth during the Archean eon, 3 Gyr ago. At that time, one of the more widespread life forms on the planet were purple bacteria. These bacteria are photosynthetic microorganisms and can inhabit both aquatic and terrestrial environments. Here, we use a radiative transfer model to simulate the visible and near-infrared radiation reflected by our planet, taking into account several scenarios regarding the possible distribution of purple bacteria over continents and oceans. We find that purple bacteria have a reflectance spectrum that has a strong reflectivity increase, similar to the red edge of leafy plants, although shifted redward. This feature produces a detectable signal in the disk-averaged spectra of our planet, depending on cloud amount and bacteria concentration/ distribution. We conclude that by using multi-color photometric observations, it is possible to distinguish between an Archean Earth in which purple bacteria inhabit vast extensions of the planet and a present-day Earth with continents covered by deserts, vegetation, or microbial mats.