A solar SCIDAR (scintillation detection and ranging) technique is proposed for measuring the heights of turbulent layers using the Sun itself, instead of the binary stars used in night-time SCIDAR. A formula for the technique is derived under various assumptions: uniform intensity distributions on the solar surface and sparse speckle distributions on the image plane. It indicates that the cross-correlation of scintillation shadows yields peaks at positions corresponding to layer heights, although the shapes of peaks are blurred by both an extended seeing disc and a finite-sized field stop. A knife-edge effect caused by field stops in an observational system is also described, which yields another peak at the centre of the correlation plane. Observations were conducted using a solar SCIDAR system developed at the Hida Observatory in Japan. In many results, peaks on correlation planes demonstrated a contrast high enough for them to be distinguished from the background. Most of the distances to turbulent layers derived from the scintillation peaks were found to be between 2.5 and 3.5 km. Use of a high-performance adaptive-optics system upstream of the SCIDAR system is suggested in order to provide better results.