As someone who raises anoles myself I would like to offer some suggestions if you want your little buddy to thrive...
I hate to say this but based off of this picture I have some good news and bad news. The bad news is I don't believe he will live very long in that setup...maybe a couple of months tops, but the good news is you can easily change that !
Although anoles are very cheap lizards, they make really amazing pets with unique personalities that can easily be tamed, but in order for them to be tamed and live a stress free life you will definitely need to make some changes and be prepared to spend at least $100-$150.
First I want to critique your setup based off of what I see in your picture and let you know what I would change if you plan to keep this enclosure (not recommended), and then I will provide a list of items that I would recommend getting if your budget allows it.
First, and most importantly I can't tell what kind of light you have there but you need to use that light fixture for a heat bulb only (which it looks like you do) but you must must must get a UVB fixture strip and bulb like this in order to provide him with UVB lighting...without UVB he won't last long at all.
You also need to get rid of the heat mat because this is useless for anoles because they do not like to stay on the ground...they have to be able to climb as high as possible inside the enclosure otherwise they are just going to be stressed 24/7...speaking of climbing, I may be wrong but those green branches look extremely thin and not really suitable for climbing, and if he can't climb he will be stressed out, so I would suggest getting a couple fake plants that attach to the glass with suction cups (some Walmart have them for like $5 usually found in the same aisle as the hamster and bird toys) or you can find them online here
Now, if you really want to give him a stress free life you need to just toss that enclosure altogether...like I said, anoles like to climb so having a vertical enclosure (taller than wider) will do wonders for him. I am not sure of your budget but you can find a vertical enclosure starting at under $40 like this one or a little bigger for around $70 like this one
You will also want to provide him a mixed diet of crickets and meal worms...you can get a 50ct of mealworms for about $4 at petsmart or petco and just feed him a couple a day in a small feeding dish (as long as you keep them refrigerated they should stay alive for usually about a month and then they typically can live up to 2-3 days once you put them in his enclosure) You can also get live crickets as well and just drop 3 or 4 in there each day.
You generally only need to mist him once in the morning and again sometime in the early evening around 5pm. Now, once you have him living in a "stress free" environment he will be much easier to tame.
If you want to have him tame quickly just do the following...for the first couple of days try to feed him and mist him around the same time every day (sometime in the early morning hours around breakfast), so he gets used to seeing you at these times) and then after a few days slowly reach in and grab him (gently!) and remove him from his cage. He will squirm a bit obviously trying to get away but after a few moments he will tire out. Once he is calm, hold him firm enough where we can't get away, but don't squeeze him, and you want to begin to gently and slowly pet his back (try to avoid petting his head until he gets used to you), but pet him for about 5-10 minutes until he starts to get fussy again and then put him back in his cage.
Do this consistently for about a week repeating this process and before you know it he will begin to interact with you and learn to trust you (I have 3 chilling on my shoulders as I am typing this).
Anyway, I hope this helps! Good luck with him!!!