I made a simple app which uses php to access my database. My question is, because the php script has db connection string in it, can someone go to the page where the script is and read that script(thus getting the connection string)?
Your PHP is processed server side and assuming your webserver is setup correctly it should never download.
That said its best to put Connection strings or other secure information in an file not under the webhost and call it via fopen() or a similar process so even if it has an issue it wont display the text because the contents of the file have to be read programmatically to be consumed.