The currency is up by 0.7% at .7592 per dollar as of 7:56 a.m. ET.
The RBA lowered its benchmark interest rate to a record-low of 1.50% earlier on Tuesday, as most economists were expecting.
The central bank's board noted "that prospects for sustainable growth in the economy, with inflation returning to target over time, would be improved by easing monetary policy at this meeting."
"The negativity toward the US dollar is offsetting the rate cut in Australia and further evidence that the UK domestic economy is taking a hit in the immediate post-referendum period," wrote Marc Chandler, the global head of currency strategy for Brown Brothers Harriman.
"On the face of it, the rate cut would appear to push the central bank back into a holding pattern, for what may be an extended period," he added.
As for the rest of the world, here's the scoreboard as of 7:56 a.m. ET:
- The Japanese yen spiked up 0.7% to 101.72 per dollar after Japan's Cabinet approved a new economic stimulus package on Tuesday worth more than 28 trillion yen ($275 billion). The measures include only 7.5 trillion yen ($73.5 billion) in government spending, which will be spread over a number of years. The rest is meant to be subsidized lending and private sector spending, according to AP's Mari Yamaguchi.
- The British pound is up 0.5% at 1.3237 against the dollar despite the latest data showing that Britain's construction sector shrank post-Brexit. Construction PMI came in at 45.9 in July, below June's reading of 46.0.
- The US dollar index is weaker by 0.3% at 95.43 ahead of a quiet data day. Auto sales will be released throughout the day.
- The euro is stronger by 0.3% at 1.1193 against the dollar. Earlier in the day, it touched 1.1204 - the first time the currency ticked above 1.1200 since June 24, the day after the Brexit vote.