No
Why? Because you should be inside at home! #StayHome
But if you absolutely had to go out to get groceries, medication or other essential travel, No, you don't need a jacket.
Based on the weather in Austin, TX, USA as of June 2, 2020 5:40am local time.
Now
Partly Cloudy
Temp: 70°F21°C
Wind: 2 MPH3 KPH
Precipitation: None
Temp: 70°F21°C
Wind: 2 MPH3 KPH
Precipitation: None
Today
Next 2 hours: No
Next 4 hours: No
Next 8 hours: No
Tomorrow
No
Humid and partly cloudy throughout the day.Low of 69°F21°C, High of 89°F32°C
Wind: 6 MPH9 KPH
Precipitation: 19% rain