No, the SMS protocol has no provision for a return receipt. (It was designed to be used with pagers, which couldn't transmit back, so they couldn't let the sender know anything.)
If you want a return receipt, your best bet is email - and if the recipient chooses to send a receipt (some email apps allow you to choose whether to do so or not) you'll get an email back. But it's a bet, not sure thing. The recipient could choose not to, the recipient's email app may ignore the request, it may send a return receipt as soon as the email with the request is received, whether it's opened or not. It usually only works in a business environment, where everyone's email program is set to return the fact that the email was opened. (And even that can't assure you that it was read, only that it was opened.)