Selecting a random node from a list in C

I have a list and I want to randomly select a node from it. As it's not an array I don't know in advance its length. Is there a way to select a node randomly (with homogeneous distribution) without having to scan the whole list in order to get its length?

Here's the code I use for my list:

struct mynode {
    in_addr_t paddr;
    struct mynode *prev, *next;
};

struct mylist {
    struct mynode *first, *last;
    char *name;
};