Did you harden it off before putting it outside? Sounds as if it has had a shock with the change of conditions. Presumably your kitchen was not 100 f and full sun so the poor thing has had a nasty surprise. I can't really recommend what to do because I have no experience of a climate like yours but I would guess it needs to be watered and shaded to give it a chance to adapt.

I've had great success rooting cuttings from sprigs of rosemary purchased from the grocery store. It's an inexpensive way to have your rosemary and eat it too, lol... Here's how: Buy a bunch of cut rosemary. Cut off 1-2" of the tops. Cut where the stem transitions from supple green to woody. Dip the cut ends into some hormone rooting powder. There are many different brands, inexpensive and widely available at your nursery: Stick the cut ends into a pot of well-wetted potting soil. (I usually put six or eight to a pot; wet the soil BEFORE you put the cuttings in.) Put the pot in the sun and keep the soil well-dampened but not soaked. Your cuttings will root. As they do, lessen the watering. Remember, rosemary is native to hot, dry climates. In the meantime, use the rest of your rosemary sprigs for cooking. Yum.

Water after transplant once and thoroughly. Then watch and wait.

OK, I'm in the minority here. I do root cuttings in water (usually I use "water beads). I wrote up something about that last year. There are a few caveats for doing this. You need to root them in an opaque container. Light inhibits root formation. You need to aerate the water at least daily (several times a day is better). You can do this with a drinking straw or a thin piece of clear vinyl "aquarium" tubing. Blow bubbles in the water at least once daily. If you want to automate the process, running a small aquarium air pump for 1 or two minutes 4 to 6 times a day is perfect. Once the roots are developing, transplant to seedling starter mix or some kind of "potting mix." Oregano develops roots quickly, usually within a week or so. Thyme and sage take a couple of weeks, and rosemary is slower and can take up to 4 to 6 weeks to develop roots ready to transplant. Dipping the cuttings into "rooting hormone" powder can help things go quicker. Most rooting hormone mixes say not to use the stuff on herbs you will eat. I'm not sure why that is. Another option is "willow bark tea," which is a natural source of the hormones that promote root growth. Edit: Here's a link to the thread I posted last year about my methods: I tried a new way of rooting cuttings. Thought I'd share.