Yes, you can.
Here is an example from the documentation:
//Check for existance of a file
var document = Ti.Filesystem.getFile(Ti.Filesystem.getApplicationDataDirectory(),'custom.txt');
if(document.exists()) {
//file exists , do something with it
}
//Writing data to a file
var document = Ti.Filesystem.getFileStream(Ti.Filesystem.getApplicationDataDirectory(),'custom.txt');
document.open(Ti.Filesystem.MODE_WRITE);
document.write('New Data for File');
document.close();
For more information see the Filesystem documentation: Ti.Filesystem.File