There is no direct way that I know of. But it is possible, round aboutly.
You need a contacts app that is capable of importing and exporting contacts both as vCard (.vfc) and .csv file types. Google Contacts will do this.
First, you need a sample spreadsheet from the app that is going to do the converting. You get that by creating a few contacts, exporting them as a .csv file, then importing that file into your spreadsheet.
Compair the structure of the original and the sample. Your original must have the same fields and column order as the sample. Re-arrainge, or do a lot of copy and pasting of columns to make it happen. {depending on the app you choose, it might be smart enough to figure this out on it's own based on column names, so importing a few addresses first might be worth trying}.
When you are ready, you export your spreadsheet in Excel as a csv file, then import that file into the converting app/service.
Check to make sure it worked.
Now use the converting app to export all your contacts as a vCard file.
You can import this file to Contacts either by going to icloud.com in a computer browser, or by mailing it to yourself and tap-holding on the attachment for an import to Contacts option.
Or, you could stop with the Google Contact import and use that instead of iCloud. You lose a few features in the Contacts app, but gain greater flexibility across platforms.
It's possible there is an app somewhere in the App Store that will do this more directly, but I don't know of one.
Good luck.
Notes: Unlike csv files which have only a loose definition and is not specifically meant to support contacts, the vCard file type was designed for storing and transferring contact information. For that reason fewer and fewer contact apps are supporting csv import/export. As usual, Apple is well ahead of the curve on abandoning older, inferior standards.