The ACB asked the Telugu Desam Party (TDP) legislator to appear before 5 p.m. on July 6.
The ACB had summoned him for questioning last month but he failed to respond. He later sent a letter to ACB, seeking 10 days time to appear before it, citing ill-health.
Veeraiah, who represents Sattupalli assembly seat in Khammam district of Telangana, had stated couple of days ago that he was ready to appear before ACB and that he would fully cooperate with the investigations.
The ACB had last month quizzed V. Narender Reddy who was the TDP-BJP candidate in the Telangana Legislative Council elections.
TDP legislator Revanth Reddy was arrested by the ACB on May 31 while he was offering Rs.50 lakh as bribe to nominated member Elvis Stephenson reportedly to induce him to vote for Narender Reddy.
The ACB, which had laid a trap on a complaint by Stephenson, also arrested two aides of Revanth Reddy.
All the three were granted bail by Hyderabad High Court on Tuesday.
The Supreme Court on Friday dismissed ACB's petition to cancel their bail.