Yes – there is. The s at the end of “suis” liaise with the a at the beginning of américain. You should pronounce it “Je sui-zaméricain”, with a Z sound.

You would not have a liaison in “Je suis désolé”, since the first letter after the s of “suis” is not a vowel. The s would then be silent.

As you may know, in French some letters are silent when they are at the end of a word, for example “s”, “t”, “d” and “p” (this is what I was taught when I was young).

So, the word depot is pronounced as if the final t were not there, and the same happens with suis, il entend et coup, just to give you a few examples.

However, because of the thing called liaison, when a word ending in “s” is followed by another word starting with a vowel, the consonant is slightly pronounced and for this reason you say “Je sui- zAméricain” as much as you say “Je sui- zItalien”, or “Je sui- zEspagnol”.

EDIT

I forgot to add another frequent expression where you need to create such a liaison, that is pas encore.