No, Daniel's right. Or the true answer is yes, any time you throw something up into the air, it's in orbit. It's just that the orbit intersects the Earth's surface. Orbits are (to a good approximation) closed ellipses, so anything shot from the Earth's surface will come back to surface level no matter how fast you shoot it.
Another way to think about the problem: An orbit is determined by both the energy and angular momentum of the object. (A circular orbit has the highest angular momentum of any orbit with the same semimajor axis.) From a point injection of these, like from a gun, you can get enough energy but never enough angular momentum to get the perigee higher than the Earth's surface. For that you need some tangential thrust (at a location that's not the apogee).
The most energy-efficient way to get into orbit consists of two tangential impulses. The first one raises the apogee to the desired height, the second one is injected at apogee to circularize the orbit. (Though it's strictly only applicable for changes in orbit, not from launches from the ground: http://en.wikipedia.org/wiki/Hohmann_transfer_orbit)
Another way to think about the problem: An orbit is determined by both the energy and angular momentum of the object. (A circular orbit has the highest angular momentum of any orbit with the same semimajor axis.) From a point injection of these, like from a gun, you can get enough energy but never enough angular momentum to get the perigee higher than the Earth's surface. For that you need some tangential thrust (at a location that's not the apogee).
The most energy-efficient way to get into orbit consists of two tangential impulses. The first one raises the apogee to the desired height, the second one is injected at apogee to circularize the orbit. (Though it's strictly only applicable for changes in orbit, not from launches from the ground: http://en.wikipedia.org/wiki/Hohmann_transfer_orbit)