She was also a disqualified driver at the time.
While in police custody, she caused damage to police property to the value of $195.
Raukawa Simon, acting for Rivers, said she was not bringing in a wage and would be unable to pay reparation for the police property or the power pole.
Judge Dugald Matheson said Rivers had significant alcohol and methamphetamine issues which had continued despite bail conditions prohibiting her from using those substances.
She was at risk of further offending if such substance abuse continued, but her probation report showed she appeared to have no motivation to change or regard for her own safety, or that of others.
"You need help, but it's you that has to pick it up and run with it".
The drink driving offence was her third in 15 months, and although there was substantial damage done to the power pole and at the police station, reparation was beyond her means.
Jail was the only option given her lack of insights and high risk she posed, he said.
Rivers was sentenced to four months in jail with six months post release conditions.