As Audioguru said, you can use an allpass network. You could possibly do this more easily digitally (A/D, delay, D/A) but I'm basically an analog guy, so I did a little research...
I found a program called
**broken link removed**. I downloaded it, and by playing around a little, I got it to give me seven different implementations of the same transfer function, which does what you want... except for one thing. For some reason, some of the implementations have inverted outputs.
Filter free will give you frequency response and schematics. To satisfy my own curiosity, I have redrawn and simulated two of the implementations (below), with a plot of their respective phase plots. I got rid of the inverting output stage that the program had added to the upper circuit.
The upper circuit (out2) has slightly flatter amplitude response. Out1 has about 0.2dB dip around 1kHz. This may be because I rounded the component values to 2 places past the decimal.
If you have any design or analysis experience, I encourage you to play with Filter Free. It's pretty cool.
BTW, these circuits will give you 250usec delay from DC 1.1kHz, and out to a couple of KHz, depending on how much delay variation you can tolerate.
PS I want to make it clear that the schematic below contains
two separate circuits that do the same thing.