You can first name the capability of managing this taxonomy. Then add the capability to the administrator, like this:
register_taxonomy('servicecategory',
array ( 0 => 'servicecategory',),
array( 'hierarchical' => true,
'label' => 'Specialties',
'show_ui' => true,
'query_var' => true,
'rewrite' => true,
'show_in_nav_menus' => true,
'show_admin_column' => true,
'singular_label' => 'Menu',
'capabilities' => array ( //giving a name to the capability
'manage_terms' => 'manage_servicecategory',
'edit_terms' => 'manage_servicecategory',
'delete_terms' => 'manage_servicecategory',
'assign_terms' => 'manage_servicecategory'
)
)
);
$role = get_role('administrator');
$role->add_cap("manage_servicecategory");