One easy option is to merely draw a path with rounded end caps.
- Switch to Outline Mode (View > Outline)
- Turn on the Smart Guides (View > Smart Guides) if they aren’t already on
- Ensure the center marker is enabled in the Attributes Panel:
Using the Line Tool, merely draw a path from the center of one circle to the other. The Smart Guides will tell you when you are at the center with the cursor.
Then merely adjust the stroke weight to match the width of the circles and tick the Rounded End Caps option on the Stroke Panel