Can you send a ballistic missile into space?

The Aegis BMD system, coupled with the RIM-161 Standard missile (SM-3), has also demonstrated a limited capability as an anti-satellite weapon against satellites in the lower portion of low Earth orbit. On February 20, 2008, USA 193 was destroyed by a group of Aegis ships in the Pacific, out of concern of that satellite's hydrazine payload contaminating land area upon re-entry from an uncontrolled orbit. The launching vessel was the USS Lake Erie, and one SM-3 missile was used. Interception was at an altitude of 133 nautical miles (247 kilometers).

As 100km is considered to be space the answer would be yes check related link for more info