Cat won't pee in litter box

So, I rescued my cat (Carlos) from the Humane Society and the reason Carlos was given up was because he wouldn't go pee in the litter box. He's a healthy, neutered cat who's about 6 months old. The vet (I was able to keep the same vet) said that he was healthy all through his life and there should be no reason why he won't go pee in the litter box, but he will go poo there. So far, he's only peed on a blanket, and it's only him and I and I feel really guilty locking him in the bathroom (it's the only room that isn't carpet) all day while I'm at work. 

Try adding at least one more litter box.  It's possible Carlos wants to pee in one box and poop in the other - that's not uncommon.  The rule of thumb for the number of litter boxes is one per cat plus one extra, so you would need two.

There are some other things you can do as well.  Consider using Dr.Elsey's Cat Attract Litter .  The texture of the litter plus an herbal additive encourages cats to use the box.  Here is their website:  http://preciouscat.com/product   You only use it until Carlos is reliably using his box and then gradually shift over to a regular litter.

Below are some articles that should be helpful.
[article="32366"]How To Solve Litterbox Problems In Cats The Ultimate Guide  [/article][article="22302"]Litter Box Location Secrets  [/article][article="0"]Litter Box Maintenance  [/article][article="31189"]How To Choose The Right Cat Litter  [/article]
An important aspect of the solution is ensuring that any area that's been soiled has been thoroughly cleaned with an enzymatic cleaner.  These break down the urine molecules so cats' sensitive noses can no longer detect it.  In turn, cats don't keep returning to the same spot under the impression it's okay to go there.

There are a lot of enzymatic cleaners on the market.  Many of our members recommend Nature's Miracle but this amazon search gives you some idea of what's available:  http://www.amazon.com/s/ref=nb_sb_n...ymatic+cleaners+cat+urine&tag=&tag=thecatsite  

It was very kind of you to adopt Carlos, knowing of his litter box avoidance.  This is one of the main reasons cats are surrendered to shelters, often with owners not really trying to resolve the issue.  Bless you for taking this boy in!  Fingers crossed that he's soon using his box.  

Edit to add:  I just noticed this was your first post here at TCS.  Welcome!