The influence of DC current annealing on magnetic properties and the frequency dependence in the range from 0.1 to 20 MHz of the giant magnetoimpedance effect (GMI) of glass-covered amorphous microwires were investigated. Under a certain annealing condition (10 min annealing with applied current Ia=110 mA), the maximum change of impedance was about 200% with a maximum slope sensitivity of 0.26%/Am-1 . Further treatment with increased current resulted in a decrease of the maximum MI ratio. Meanwhile, annealing can produce short-range order relaxation and consequently improves the sample's soft magnetic properties. We also found that the GMI ratio increased due to the enhanced induced anisotropy with increasing current under the same Joule energy.