From the MediaWiki documentation:
By default anonymous uploads are not allowed. You must register and logon before the upload file option appears in the toolbox.
And then from configuring uploads:
Is there a way to allow users to upload files without logging in?
That'd be a great help for corporate environments where only a limited number of people can access the wiki (server) anyway...
SpecialUpload.php file in the includes folder
Comment out the following two lines:
$wgOut->errorPage( 'uploadnologin', 'uploadnologintext' );
Now users will not have to login to reach the upload form.
Simpler method, modify
$wgEnableUploads = true;
$wgGroupPermissions['*']['upload'] = true;