While there would be no record of a conviction, if someone searches deep enough, they will likely find a record of the arrest. Oregon law does allow you to get arrest records set-aside (or "expunged").
One year after the date of any arrest (if no accusatory instrument was filed), or at any time after an acquittal or a dismissal of the charge, you can motion for the arrest record to be set aside. Either way, you meet this qualification under the facts you have posted.
You also cannot have been arrested for anything else in the past 3 years (other than motor vehicle violations) and your arrest cannot have resulted in a DUII diversion program.
Here's a link to ORS 137.225, which is the statue that governs set-asides: http://www.leg.state.or.us/ors/137.html
Also, here's a link to a guide I wrote on the subject: http://www.avvo.com/legal-guides/ugc/expungement-101-five-easy-steps-to-see-if-you-qualify
My responses to posts on AVVO are not legal advice, nor do they create an attorney-client relationship. In order to provide true (and reliable) legal advice, an attorney must be able to ask questions of the person seeking legal advice and to thus gather the appropriate information. In order for an attorney-client relationship to exist, you and I both have to agree the the terms of such an agreement.
If you are concerned you can contact an attorney or investigator to run your record for you. You can also head to the Multnomah County Courthouse, second floor, and use the public OJIN terminals to search your Oregon record for free. At least then you will know what's there. Good luck!
Oregon's expungement law makes it possible to set aside an arrest record in a situation where the case did not result in a conviction. In many cases, expungement is possible even where there was a conviction. The procedure is governed by ORS 137.225. We assist clients in setting aside records of arrests and convictions all the time. Upon the granting of a motion to set aside, all public records of the matter are sealed and the arrest (or conviction) is legally deemed not to have occurred. For further information, feel free to contact our office.