Instead of a single resistor R1 use different resistance values for charging and discharging the capacitor. You can use diodes to separate the current directions.
Adjustable duty cycle without changing the frequency very much can be achieved by replacing R1 with this:
47 kOhm potentiometer has been chosen because it's generally available. Have a linear scale version.
You have only plusminus 5V operating voltages. The voltage drop in 1N4148 is a little unpredictable and it's variance can be too large, if you expect high precision results. In that case you should use mosfet switches to charge and discharge C1 through resistors.