It is possible to use a rainwater tank for drip irrigation. In fact, this is probably one of the only automatic ways to use a rainwater tank without a pump. Depending on the water level in the rainwater tank, the duration and frequency of watering may need to be adjusted.
The water level in the tank can be determined by connecting a short hose (like the green one below), holding it up in the air with the open end facing up, turning the tap on and finding the height at which you can see water in the hose but it doesn't flow out. You may need to wait until the hose has filled and the water level has stabilised, usually a few seconds for a 2 m long hose.
The yellow translucent pipe leads to a fern garden and a garden surrounded by brick paving, both for drip irrigation.
I installed drip irrigation for two vegetable gardens. (I was experimenting with killing the weeds in the lawn in this photo.)
Initially, I had a hose running across the lawn to this drip irrigation. This meant I had to disconnect it every time the lawn mower came. One time, I forgot to reconnect it, so when the timer turned on we lost most of the rainwater. Whoops. Therefore, I installed a hose under the lawn. Luckily, I had previously installed a stormwater pipe from a soakwell, which I could use as a duct. (I originally installed it as overflow from the soakwell, but this was made redundant by the rainwater tank.)
Combined with the bore irrigation, we are able to successfully grow chilli plants, capsicum, leeks and other vegetables.