rmx Spinebot's answer is correct. I just want to add a little more because I think it might be difficult to understand just the words. For example, the following rig is possible:
The controller bone you mentioned is probably supposed to be farther away than the bone you want to move, so I created this example based on that assumption. In this example, the bone you want to move with the controller bone is constrained by an IK constraint, and its IK target bone is set to the Controller bone. This way, the bone you want to move has its own angle of rotation, but changes its angle in response to the movement of the Controller bone.
Here's a more advanced example:
In this example, the IK-target bone is a child of the IK-holder bone, which is rotated 90 degrees. Also in the transform constraint options, the Local option is enabled. This way the local transform of the IK-target bone will be modified by the movement of the Controller bone. This allows the IK-target bone to translate in a 90-degree rotated direction, i.e., upward, when the Controller bone translates to the right.
Here is the Spine project file where you can see this rig:
