The phrase "to run a giveaway" means to organize and manage a contest or event in which something is given away for free to participants. Full definition
If you wish for me to host and run a giveaway for you without a review, the fee is $ 60, or free with a large ad purchase in the sidebar. (justaddcloth.com)
I know you have been potty training and my husband and I are currently running a giveaway on a potty training video on my husband's blog. (thenaturalmommy.com)