Most cellular carriers provide a special email address you can use to forward an email as a text message to your phone.  The format is typically [your phone number]@[gateway name].  So as an example if your cell number is 555-234-4343 and  you're using AT&T you can send an email to 5552344343@txt.att.net and it will be sent as a text.  See below for a list of various carrier names and gateways.  If these don't work, contact your cellular service provider and ask them to provide the details.  They may treat these with lower priority so they may not arrive as quickly.

If you need to guarantee faster delivery of texts, search Google for "Email to Text Gateway" and you can choose from several providers like Twilio or ClickSend for example.  They charge a tiny fee per text - typically 1-2 cents or less - and guarantee quick delivery.