I want to paint an abstract on a canvas tarp & hang it outside
You can use spray paint or acrylic latex paint.
You could spray paint it!
If you use acrylic paint, you might need to add some fabric medium to make it flexible.
There is an acrylic paint that you can put on fabric. However acrylic paint may not hold up in the outdoors. Spray paint is an option but it will make your fabric stiff where the spray paint is applied.
This looks like a good article about using a drop cloth and making it into an outdoor rug. https://pin.it/qqoz7jrkdcn2jw