She had arrived at a running club meeting in Kings Heath when three men demanded she hand over her car keys before using a stun device on her, police said.
She alerted a passing van and the men ran away.  She was left "shaken, bruised and with burns", the club said.
There were similar reports between 5 and 10 February.
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West Midlands Police said there were six reports of alleged assaults involving "small stun devices" in Moseley, Kings Heath and Acocks Green.
It is not yet clear whether the incidents are linked.
Four teenage boys, two aged 15 and two aged 16, were arrested and bailed in connection with a robbery in Acocks Green on 5 February. Witnesses are being urged to come forward.
A post on Kings Heath Running Club's Facebook page said: "There was a serious incident prior to club run last Thursday.
"It was an attempted car theft by three young men who demanded a runner's car keys.
"She refused and an electric Taser device was used on her during a physical struggle.
"She was shaken, is bruised and has seen a doctor who has assessed the burns left by the Taser.
"This was a random event - the runner took no risks in parking her car on a well-lit road next to the school."

The left-hander made 114 not out after the start of play was delayed until 14:00 BST because of a wet outfield.
He shared a stand of 142 with Kumar Sangakkara, who was caught behind off Jake Ball for 83 soon after tea.
Pace bowler Ball claimed 3-77, but Surrey, having followed on, reached the close on 297-5, a lead of 76.
Harinath scored 568 runs in eight first-class appearances for Surrey last summer, including two centuries.
He again showed a clam temperament to hold the innings together with one six and 15 fours after Rory Burns (17) was lbw to Ball in only the second over of the day.
Sangakkara also looked in good touch before he and Steven Davies departed in similar fashion in the same Ball over.
Jason Roy made a typically assertive 37, but was then lbw to Brett Hutton, leaving Harinath to bring up his century with a sweep for three off Samit Patel.

The advert from the Northamptonshire Police & Crime Commissioner (PCC) called for someone who was "resolutely client-centred and victim-focused".
The campaign group said PCCs were "serial offenders" in using "jargon".
Adam Simmonds, PCC, said: "The best communicators talk to people using the type of language they understand."
The existing chief constable, Adrian Lee, will be leaving the force in July.
The candidate information pack said the force was looking for an "agent of change" who can get "client-side" and "is a pioneer in blue-light collaboration".
Steve Jenner, spokesman for the Plain English Campaign, said: "The sentence that 'our chief constable must be able to see beyond the horizons of convention to make the paradigm shift' is a prime example of 'ploddledegook'.
"Police and crime commissioners seem to be repeat offenders in this regard for their mangling of the English language and this advert is borderline criminal.
"Senior police officers are probably used to this kind of jargon so they will understand it but the danger is they use it when they talk to the public."
The information pack also said the chief constable should not just issue "management speak from above" because "inevitably such statements of corporate aspiration can feel like yet another list of jargon and management-speak".
In response to the criticism, Mr Simmonds said: "Anyone who knows me knows I am a straight talker, but it is a fact, highlighted by the Plain English Society, that senior police officers have to understand the type of language used in the advert.
"What I want from our next chief constable [is] someone who can talk to politicians and judges as easily as they can their own staff and members of the public."
The deadline for applications is 1 June and the job's salary will be up to Â£150,000.
A woman was attacked with a stun device during a car-jacking in Birmingham - the sixth such attack in as many days.
[NEXT_CONCEPT]
Opener Arun Harinath hit an unbeaten century as promoted Surrey avoided the prospect of an innings defeat on day three against Notts at Trent Bridge.
[NEXT_CONCEPT]
A 26-page job advert for a chief constable has been described as "ploddledegook" by the Plain English Campaign.