How can I model solid rods in STAAD.Pro ? Can I design these as per AISC code ?

Currently there is no database available for solid rods in the STAAD section database. However if you need to define one, you may click on "Define" button within the "Properties Whole Structure" box and use the parametric Circle shape as shown next.

There is no way to design these in STAAD.Pro as per the AISC code. However here is something that you may consider doing

If you have to design the rod section, instead of modeling the rod as shown above, define it as a user table pipe section by going to Tools > Create User Table > New Table > select section type as Pipe > Click on OK. One the user table of type Pipe is defined, click on the Add New Property button to define a pipe section. Specify the Inner diameter to be a very small value so that the pipe closely approximates a rod. This would adequately model the stiffness due to the solid rod. You may subsequently design the member and STAAD.Pro will be able to design the section following the rules applicable for pipes.