We demonstrate how local heating by an electric current can induce and reorient the exchange bias on a nanoscale. In our experiments we use point contacts ~10 nm in size to inject current densities as high as 10 into F/N/F/AFM exchange-biased spin valves (EBSV) where two ferromagnetic (F) layers are separated by a nonmagnetic (N) metal spacer and one of the Fs is biased by an adjacent antiferromagnetic (AFM) layer. At low currents the spin valves exhibit the usual giant magnetoresistance (GMR) when two F layers switch from parallel to antiparallel orientation. At highest applied currents the Joule heating in the contact becomes significant and in combination with static magnetic field can induce and repeatedly reorient the exchange bias in a small contact volume . The strength of exchange bias induced in the point contact was found to depend on the polarity of the applied current. We tentatively attribute this polarity dependence to spin-transfer torques arising near F/AFM interface at high currents.