This implementation uses a high-pass filter at the non-inverting input to generate the phase shift and negative feedback to compensate for the filter's attenuation.
At the corner frequency ω=1/RC of the high-pass filter (i.e., when input frequency is 1/(2πRC)), the circuit introduces a +90 degree shift (i.e., output is in quadrature with input; it is delayed by a quarter wavelength).