There is a wealth of evidence for the presence of "dark matter". Before I get into it, dark matter is simply stuff that we can't see that doesn't seem to interact with the type of matter that we see around us.
Also, there is no reason that dark matter can't fall into a black hole; it does, in fact, interact gravitationally. The type of accretion onto a supermassive blackhole like the one in the centre of our galaxy would be called Bondi-Hoyle accretion, think of it like the pacman approach to sucking up matter. Whatever paths intersect the event horizon are consumed. Moonbogg's post is mostly correct, however there are a couple of ways which dark matter could lose angular momentum (more likely it actually gains it, but that's a relatively recent problem to be solved) such as dynamical friction (wiki it, should be there).
Now, dark matter:
Our best evidence for dark matter is an amalgamation of big bang theory with the extremely good observations of the cosmic microwave background by WMAP. The details of which are a bit too involved to get into on a forum post, but there are many resources out there to learn why this is true. -- Not to say it is necessarily correct, but that it is our best fitting model of the universe.
The first hint of dark matter came with rotation curves of our galaxy and then others. A rotation curve is a measure of the radial velocities of HII regions as a function of galactocentric radius which we can get by measuring the doppler shift of the 21cm hyperfine hydrogen spin flip transition. A simple application of galactic gravitational potential theory tells us that if the mass of the galaxy were contained in the visible material then this rotation curve should drop off like 1/r. Instead, we see rather robustly that these curves remain constant implying there is a large amount of mass in the outer regions of galaxies (again, potential theory). This has led to a quantity called the mass to light ratio which describes how much mass (measured by rotation curves for instance) compared to the amount of mass measured by the luminous matter.
So why can't all the mass be in things like black holes, brown dwarfs, neutron stars etc? We thought of this pretty early on, they were coined MACHO's (massive compact halo objects). We came up with a lot of theory to try to predict how much mass could be hidden in objects like this and it just doesn't work, we also can do some statistics given our local neighborhood and the numbers don't match up. The WMAP results really put a nail in this coffin too.
Maybe they aren't really big objects, but lots of tiny little objects that we can't see, like neutrinos. Thought of this too, this theory was called hot dark matter, again, too much detail here so I'll skip it. Suffice to say, WMAP kills this theory.
There are other sources of evidence for dark matter, such as gravitational lensing (both strong and weak) and the prime example, the bullet cluster (seriously, look this one up its very cool).
Anyone care to explain Hawking Radiation, I've taken up too much space on this post already....