Yes, any BLE device can act as a beacon as long as you can control the advertisement payload. Beacons are a subset of BLE devices. By definition, beacons are BLE devices that are constantly/continuously advertising data that are relevant to other remote devices, usually containing information about its location/proximity.
So to answer your question, as Mike Petrichenko suggested, all you need to do is alter your advertisement data to something that is relevant to remote devices. If you still need to send your current adverts, then you'll need to alternate between sending the current advert data and the relevant beacon data. You can control the frequency at which each data is sent depending on your application (e.g. For every 10 adverts of your current payload you can send the beacon advert if it's less frequently needed).
Some references:-
What Are Beacons and How Beacons Technology Works
5 Things You Need to Know about Beacon Technology
What Are Beacons, and How Are They Used in IoT Applications
I hope this helps.