There is no one international sign language in common usage. Each signing linguistic community in various regions/countries has a unique sign language that is not based on the spoken language of the region/country. For example in the US/Puerto Rico and most of Canada American Sign Language is the predominant sign language used among Deaf people and their hearing allies, families and people who may have some relationship to the Deaf community. American Sign Language is not based in English and has its own grammar etc. To further illustrate this British Sign Language used in England primarily has no direct relationship to American Sign Language although English is spoken in both England and the US. And although Australia is an English speaking country and has a close relationship to England, Australian Sign Language is also different from British Sign Language and American Sign Language.
There is a "International Sign Language" called Gestuno which was developed primarily through efforts of the World Federation of the Deaf. The purpose of this International Sign Language was to facilitate communication between and among Deaf people at international meetings etc. This system of gestures was never intended to replace extant native sign languages. It has very limited numbers of people who know it but it is used when the World Federation of the Deaf has conferences etc.
On another level there may be a number of basic gestural signs that are shared between sign languages because these very iconic signs represent basic human functions like eating and drinking. So for example a sign like "TO-EAT" may be the same or very close to the same sign in many sign languages throughout the world. Beyond however some very basic, iconic types of signs that represent basic functions like this, there will be a very limited set of signs that are the same between and among sign languages.
And one final point. Just like English dominates the World of languages because of the economic dominance of the US many deaf people across the World will know some American Sign Language as well as their native sign language. And American Sign Language because of this relative dominance has influenced other sign languages. This dominance of ASL also leads to some adoption of ASL signs into other signed languages. But it is also true that ASL is influenced by other foreign sign languages and because of greater awareness and respect for other sign languages the American Deaf community has incorporated a good number of "foreign" signs into our sign language vocabulary. A good example of this is the replacement of traditional ASL signs for country names with the sign used in the foreign country for that country name.
Hope this explanation is helpful. It is not an easy topic to discuss without having some background in the sociolinguistics of signed languages, but I hope this cursory explanation has given you some insight and may pique your curiosity to study this question further on your own.
