While this isn’t something we see often, it is a possibility if you go about it in an ethical way. (Note: this BBC article does a nice job of outlining some of the ethical considerations of asking for money for your own travels.)
If you do decide to start a crowdfunding campaign, it’s a best practice to offer something in return- this could be some kind of creative work like a weekly emailed blog post update, or even something tangible like a coffee table book of photographs from the trip.
We’d recommend taking the time to research and evaluate your alternatives. Here’s a pretty comprehensive list of crowdfunding platforms from the Building Bridges Coalition.