In 1998, Shibata and Sasaki [Phys. Rev. D 58, 104011 (1998)] presented an approximate analytical formula for the radius of the innermost stable circular orbit (ISCO) of a neutral test particle around a massive, rotating, and deformed source. In the present paper, we generalize this expression by including the magnetic dipole moment. We show that our approximate analytical formula is accurate enough by comparing it with the six-parametric exact solution calculated by Pach\'on et. al. [Phys. Rev. D 73, 104038 (2006)] along with the numerical data presented by Berti and Stergioulas [Mon. Not. R. Astron. Soc. 350, 1416 (2004)] for realistic neutron stars. As a main result, we find that in general, the radius at ISCO exhibits a decreasing behavior with an increasing magnetic field. However, for magnetic fields below 100 GT the variation of the radius at ISCO is negligible and hence the nonmagnetized approximate expression can be used. In addition, we derive approximate analytical formulas for angular velocity, energy, and angular momentum of the test particle at ISCO.