This is a situation where calling the facility directly before you make the trip is essential, and the person to ask for specifically is the corrections officer who oversees the visiting room.
There are two separate questions wrapped into this one. The first is whether the facility has any policy about service animals in the parking lot or on facility grounds while you are inside visiting. Some facilities are entirely fine with a service animal remaining in a vehicle in the parking lot. Others have policies that restrict what can be on facility grounds, including vehicles with animals, for security reasons. You need to know which situation applies at Oregon State Correctional Institution before you drive out there.
The second question is practical rather than policy-based. Leaving a dog in a car during a visit carries its own considerations depending on weather, the length of the visit, and whether your dog is comfortable in that setting alone. Even if the facility has no objection, making sure your dog is safe and comfortable in the vehicle for the duration of the visit is something to plan around carefully.
If the facility's policy does not allow animals on the grounds at all, or if leaving your dog alone in the car is not a workable solution, the next step is finding someone who can stay with your service animal outside the facility while you visit. That is not an ideal arrangement, but it preserves both your ability to visit and your dog's wellbeing.
Call OSCI, ask for the visiting room officer, explain your situation, and get a clear answer before you commit to the trip. Getting that confirmation in advance saves you from an unnecessary problem on what is already a difficult day.