Yes. Look into the Suspension Techniques kit. Probably the most popular and best rear swaybar for 4th gen Civics. We run their bar on the '91 Civic Si that I race. Very high quality, great fitment, adjustable and good price.
To answer your question again, yes.. You can mount a rear swaybar on there. Even though it's a base model, it still uses the same basic "frame" as all the other models, including the Si. Which means it also has the mounting points for you to be able to install a swaybar. The Suspension Techniques bar that I linked bolts directly to the "frame" and the endlinks attach directly to the shock bolt in the lower control arm (meaning you don't need aftermarket lower control arms to use a swaybar).
To prove this, just look at Suspension Techniques Part Numbers. For a '91 Civic DX the rear swaybar Part Number is 51140. For a '91 Civic Si the rear swaybar Part Number is the same, 51140. It's the same exact part regardless of the model (DX or Si). Why? because they use the same mounting points which means it will work on your car.