The Sun shows a ∼10 per cent depletion in refractory elements relative to nearby solar twins. It has been suggested that this depletion is a signpost of planet formation. The exoplanet statistics are now good enough to show that the origin of this depletion does not arise from the sequestration of refractory material inside the planets themselves. This conclusion arises because most sun-like stars host close-in planetary systems that are on average more massive than the Sun’s. Using evolutionary models for the protoplanetary discs that surrounded the young Sun and solar twins, we demonstrate that the origin of the depletion likely arises due to the trapping of dust exterior to the orbit of a forming giant planet. In this scenario, a forming giant planet opens a gap in the gas disc, creating a pressure trap. If the planet forms early enough, while the disc is still massive, the planet can trap ≳100 M⊕ of dust exterior to its orbit, preventing the dust from accreting on to the star in contrast to the gas. Forming giant planets can create refractory depletions of ∼5−15 per cent⁠, with the larger values occurring for initial conditions that favour giant planet formation (e.g. more massive discs that live longer). The incidence of solar twins that show refractory depletion matches both the occurrence of giant planets discovered in exoplanet surveys and ‘transition’ discs that show similar depletion patterns in the material that is accreting on to the star.