A friend of mine said if I write a letter of recommendation, he'll sign it. I'm sure I can write a great letter. Is that okay?

No. While you can probably write a letter that will seriously shine and your friend probably knows you better than anyone, a prospective construction employer is more interested in a previous construction employer's perspective on you in their own words. If your friend worked with you, have them write the letter. While self-authored letters do get written and submitted, they are generally frowned upon when discovered.