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Benjamin Iliffe, 36, from Cambridgeshire, was sentenced at Huntingdon Magistrates’ Court to 15 weeks in prison suspended for 18 months after admitting sending the deputy Labour leader a threatening email.
Police also said they made a third arrest on Thursday over phone calls, emails and letters sent to Ms Rayner in recent weeks.
GMP said a 70-year-old man had been arrested in conjunction with South Yorkshire Police on suspicion of malicious communication and remained in custody.
He was arrested in relation to emails received on October 16, while a 52-year-old was arrested in Halifax, West Yorkshire, and bailed over abusive phone calls Ms Rayner received a day earlier.
Ms Rayner, a mother of three who is on bereavement leave, reported receiving the threatening contacts over a number of weeks.
After the first arrest, her spokesman said: "Abuse and threats of this nature don't just have an impact on Angela but also on her family, her children and her staff who are on the receiving end of these communications."
The investigation by at least three police forces comes amid increased concern over the safety of MPs and the level of abuse they receive following the killing of Sir David Amess.
The veteran Conservative MP for Southend West was stabbed in a suspected terror attack during a constituency surgery in Leigh-on-Sea, Essex.
Iliffe was due to appear before Huntingdon Magistrates' Court on Thursday.