I think to answer the question it helps to have a little background about what DNA is and how it works. In a lot of the cells in your body, DNA is like a recipe book. It provides instructions for building proteins that keep your body doing all the body things that bodies do.
For those pieces of DNA, it’s hard to imagine how marijuana would alter it. The DNA is already made and it’s pretty stable like that. But there are molecules that interact with the DNA and how it gets expressed – think of these like notes in the margins of the recipe book, but scribbled in pencil and easily erased. It would be easy for marijuana to affect those molecules and as the other links in the thread showed, it probably does. I personally would not call that “changing your DNA” because it changes something that hops on and off your DNA, rather than the DNA itself.
But there is another scenario where it could potentially change the DNA – when new cells get made, new DNA strands get made. In some parts of your body (skin, bone marrow) new cells get made very often. In other parts of your body (eg brain), new cells get made rarely, if at all. And of course when a baby is growing, every cell is new. Each time a new cell is made, and a new DNA strand gets made, there’s a chance for something to go wrong. And it seems totally plausible to me that marijuana could affect the copying-over process, and change the DNA in some of your new cells.
But can it change DNA that’s already made, in cells that are already there? Probably not. Can it change all the DNA in your body at once? Definitely not.
tl;dr: Kinda