Can I still use a Tagine that was outside for a while?

As it's not glazed I'd first consider what other than water & 'dirt' it may have been subject to & ask, "Would you eat from a plant pot in similar circumstances, no matter how well-scrubbed?"

I'd seriously consider a new tagine & somewhere indoors to keep it this time.

If all the tagine was exposed to is water and dirt then you should be fine as long as you clean it off and bake it to drive out any water. Tagines are generally unglazed on one side so will absorb water, if you don't dry it out it could crack when you try to use it. the process would be put it in a cold oven and turn it up to 170°C (350°F) for 2 hours, then turn the oven off and let it cool overnight with the door closed. The baking may tell if you have problems, if it smells nasty you'll probably want to get rid of it, if it's a normal clay smell you should be good.

If your tagine has been exposed to significant amounts of weed killer, bug killer, liquid fertilizers or other chemicals then it may have absorbed them in which case you'd want to think twice about using it. If there's been a couple of sprays around it there's nothing to worry about.

One additional piece of advice to GdD's excellent procedure: if the tagine is terracotta or other porous clay, you're going to want to get any absorbed grime out of the clay itself. This means soaking it in hot soapy water, scrubbing it, then soaking it in a couple of changes of hot water with no soap for a few hours to get the soap out of the clay. Then follow his advice for drying it.