You should be able to do this via the option_page_capability_{$option_page}
hook – like:
function wpse151616_grant_access_to_options_page_for editors() {
return 'edit_posts';
}
add_filter( 'option_page_capability_rooster',
'wpse151616_grant_access_to_options_page_for editors' );
For possible return values take a look at Roles and Capabilities. The variable part – {$option_page}
– of the hook name is substituted by the menu slug – $menu_slug
– value of your add_options_page()
call.