Both the electronic spectrum of the edge dislocation in crystalline Si and the electronic spectrum of supercell with 64 Si atoms and one oxygen atom in the interstitial position are calculated, using the density functional theory within the generalized gradient approximation. Changes in the electron density of states of the supercell with defect as well as the possible formation of magnetic order are discussed. The spin-polarized calculation confirms the possibility of magnetic order due to the considered defects with the uncompensated magnetic moments, namely, 1.25$\mu_{B}$ per supercell containing two segments of the unit-length dislocation line or 1.75$\mu_{B}$ per one O atom. The formation of magnetic moments on the dangling bonds in the dislocation core and on the oxygen impurities that leads to the additional magnetic interaction between dislocation and oxygen impurity in silicon is theoretically investigated.