How can I create two ac signals with a voltage controlled phase offset?
There are many ways to do this using samples and DAC's etc. In terms of an analog approach this can accomplished using what is known as a "all-pass" filter.  This is a filter that has uniform amplitude response with frequency but variable phase response with frequency.

The phase angle \$\theta \$ is:

\$ \theta = 180^{\circ} - 2 * arctan(\omega R C)\$

If you operate the circuit at fixed frequency but vary the RC time constant then you might  be able to get the effect you want.

The primary issue you have here is that you want voltage control over the angle.

The natural thing to do here would be to put a JFET in here and control the gate with a DC voltage.  Usually this would give you a limited variability  in the value of R and might not be that useful. However, in this case, since you have that arctan term which is highly non-limear and the fact that you only want up to \$90^{\circ}\$ of phase shift this might be doable.







simulate this circuit &ndash; Schematic created using CircuitLab

The R1 in the circuit is to bias the operating point of the RC time constant to be in the control range you'd like. (it does start out at \$180 ^{\circ}\$ after all).

You'd feed in a fixed frequency signal (sinusoid) and get a phase delayed version out.

Another alternative (if you have limited phase shift because of poor JFET control) is to cascade multiple version of this circuit each with the same control voltage. If you get only \$ 30^{\circ}\$ per stage but have 6 stages you could get \$180^{\circ}\$