is there any difference between

"i think so..."

and

"i am thinking so..."

in english.

In my opinion there is no difference in meaning.

´I think so´ is more commonly used where I live. It is used to answer questions when you are not 100% sure of something, but want to imply that in your opinion something is right, is likely to happen, is best, or you agree with what has just been said.

examples:

Will Galatasaray win? I think so. (They could lose)

Is the Chora Church this way? I think so. (You are not completely sure, but you have seen signs pointing this way)

Is tourism improving in Turkey? I think so. (You have read figures in the Turkish papers that say this, but you are not sure if the information is valid, because all your friends who worked in tourism are still struggling)

I would not use ´I am thinking so´ to answer any of the example questions above. In fact I would not use these words in everyday conversations. I use ´I think that .........´

examples:

Do you think Galatasaray will win today?

I am thinking so, Galatasaray are the stronger team (sounds weird to me)

I think so, Galatasaray are the stronger team (sounds normal)

I think that Galatasaray are the stronger team and will win. (sounds normal)