Rajasuya (Imperial Sacrifice or the king's inauguration sacrifice) was a yajna or sacrifice, performed by the ancient kings of India who considered themselves powerful enough to be an emperor. It is described in detail in the Mahabharata. Rajasuya, like the ashwamedha, would occur after the return of generals of the king (in most cases his own kinsmen, like his brother or son) from a successful military campaign. Only the king with Sovereign power is allowed to do that.
After conquering the kings of other kingdoms and collecting tribute from them, the general would invite the vanquished kings to attend the sacrifice ceremony. All the vanquished kings would in effect consider the performer of these sacrifices as an emperor. In the case of ashwamedha, the army of the military campaign is led by a wandering horse, let loose from the capital of the king who performs this sacrifice. In case of rajasuya there is no horse involved. The generals plan their route themselves. Rajasuya sacrifices were rarer than ashwamedha sacrifices, since they were riskier and costlier.
Pandava king Yudhisthira's rajasuya is the most well known rajasuya sacrifice, described in detail in the epic Mahabharata. King Satyaharischandra also performed Rajasuya yaga successfully, and was a successful emperor in ancient times. Many Chola kings are supposed to have performed this sacrifice. One of the sangam Cholas is called Rajasuyam vetta perunarkilli (i.e. perunarkilli who performed Rajasuya), for having successfully performed this sacrifice.