We have performed x-ray magnetic circular dichroism (XMCD) measurements on the iron-based superconductor Sr$_2$VFeAsO$_{3-delta}$ to study the origin of weak ferromagnetism (WFM) reported for this compound. While Fe 3$d$ electrons show a magnetic response similar to the other iron pnictides, signals from V 3$d$ electrons remain finite at zero magnetic field and may be responsible for the WFM.