Cosmic-ray electrons and positrons (CREs) of TeV energies suffer severe energy loss during prop- agation due to inverse Compton scattering and synchrotron radiation process, they are therefore very useful to constrain the local cosmic-ray sources in the Galaxy. The ability to measure CREs by ground-based imaging atmospheric Cherenkov telescopes (IACTs) has been demonstrated in the past. In this proceeding, we will present two methods – a template fit method and a tight cut method based on a two-steps-trained Random Forest (RF) – optimized for the detection and study of CREs and will report on the measurement of the CREs energy spectrum from 300 GeV to 6 TeV with the MAGIC telescopes.