To answer your question ... This is relatively simple because the only circuit components connected to GND are capacitors.
1. Add two 10K resistors in series between VCC and GND. R4 from Vcc to the midpoint, and R5 from the midpoint to GND. This establishes a reference voltage midway between your two power rails. We'll call the midpoint voltage VGND.
2. Add a 0.1 uF ceramic and a 10 uF electrolytic in parallel across R5. This decreases the AC impedance of VGND so it appears as a real ground at the oscillator frequency. BTW - WHAT is the desired oscillator frequency? As noted above, the LM358 does not perform well at high frequencies.
3. Disconnect the opamp non-inverting (+) input from GND, and connect it to VGND.
If the other half of the LM358 is available, you can use it to buffer the VGND. If you want to leave it unused ...
4. Connect the output to the inverting (-) input.
5. Connect the non-inverting input to VGND.
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