Yes you can. You can do the vinegar and baking soda test or you can do the red cabbage test.
For the former take a couple of spoonfuls of soil from your garden and put in a cup to which you add 1/2 cup of vinegar. If it fizzes then your soil is alkaline with a pH of 7-8. If nothing happens put more soil in another cup and add water to make it muddy. Then add 1/2 cup of baking soda. If it fizzes then your soil is acidic with a pH of 5-6. If nothing happens your soil is neutral
For the red cabbage test simmer a cup of red cabbage in 2 cups of water for 5 minutes. Remove from heat and leave to stand for about 30 minutes before straining the purply coloured liquid. Put a couple of teaspoons of your soil in a container to which you add a few inches of the cabbage water, stir and leave for 30 minutes. If it turns pink your soil is acidic but if it turns bluey/green then it is alkaline.
I agree a soil tester kit may give more precise gradations and you can get cheap ones but the above methods DO work. Also have a look and see what other plants you have growing. If you have rhododendrons or azaleas then it is acidic. If you have hydrangeas and the flowers are pink then your soil is alkaline, but if the flowers are blue then it is acidic.