Upvote:3
I assume that you are a national of a Visa Waiver Program country.
If your cruise to Alaska is on a private vessel, or a commercial cruise operated by someone other than an "approved carrier," you are not eligible to use the VWP. You must apply for a visa.
If your cruise to Alaska is a commercial cruise operated by an approved carrier, you must have authorization through ESTA.
If for some reason you are using "cruise" to refer to overland travel, then you do not require ESTA.