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Copy and paste the <p> tag at the beginning and end of every paragraph except add a “/” to the closing <p> tag? Coding comes with a price of your time :P Dreamweaver can do what you’re looking for. Just highlight text and press Ctrl+Shift+P. Though it’s only a 30-day trial software, unless you fork a good lump on it. There could be an online tool somewhere too.
PS, if it’s a “design” doc, you’re gonna have to loose the “easy” method attitude if you are transferring the design, as design will require more than a <p>tag haha! :D
you can place your copied text on a markdown software like iA Write and export the HTML, each breakline on iA Writer makes a paragraph (hint: you can use the markdown on github if you wanna do for free).