Yep. Select a single constructor and click "construct". (The option does not show up in constructor "fleets"). A screen will pop up and you can choose what kind of starbase you want: Military, Economy, or Influence. When you first build a starbase it is completely useless. You have to send additional constructors to the starbase to get its different systems online.

Military starbases have the best overall attack/defense options and can aid ships in their area of influence (indicated by a large circle) with long-range attacks once the ability is researched.

Economy starbases add to your planet's military, social, and research stats within the base's influence. Some later modules allow for increasing trade route revenue, starbase factories, etc.

Influence starbses have two functions. 1): They keep other race's influence (stealing planets, resources, etc) out of your space, and 2): Spreading your influence into your territory. Again, this only applies within its influence area.

The latter two can be upgraded with simple defensive capabilities but any sizable fleet can still destroy them fairly easily. You will need lots of constructors in order to keep them maintained and alive.

Hope this helps.