An unofficial CyanogenMod 13 (CM13) build for the OnePlus 3 is already available to download and install.
Since the OnePlus 3 warranty covers software modifications, you can have a try at this here. But we warned this is not a daily driver ready ROM, there are still some kinks with performance being worked out.
Moreover, this is for an advanced user as you would have to unlock your bootloader, then flash a custom recovery and then proceed with flashing the ROM. The author of the post on OnePlus forums says that there are some known issues including camera app closing after taking an HDR shot, no support for F2FS, poorer battery-life than Stock ROM and some performance constraints.
However, since OnePlus has released Kernel sources for the OnePlus 3, it won't take much time for an official CM13 ROM. If you do have the guts to port an WIP CyanogenMod 13 ROM (Marshmallow) on your device, do tell us your experience with it. You can find out more at the source link alongwith a tutorial.
Source: OnePlus Forums
