The incident at Neil McEvoy's office took place on Thursday morning. The AM said no valuables were taken but files had been "gone through".
He said metal bars had been cut to access the property at Cowbridge Road East.
South Wales Police said an investigation had been launched.
"For a long period, there has been a concerted campaign of political harassment against me," the South Wales Central AM claimed.
He said that less than 12 months ago his home had been "ransacked", with paperwork taken.
Mr McEvoy said that in the early hours of Thursday "the criminals involved went through two outside doors, down a lane, removed a screwed in hard wood cover on the back window, cut through a PVC window frame and cut through metal bars to get in the window".
"Once again, valuables were ignored in the office, but drawers were broken into and files gone through in the back office which wasn't alarmed.
"Thankfully, they couldn't gain access to the main part of the office without tripping the alarm."
"I put in place new safety procedures for staff at the end of last term, because I am aware of serious cages being rattled," he said.
"Some people would like to silence us, but this intimidation has just added to our motivation."
A South Wales Police spokesman said that the break-in was reported after 09:00 GMT on Thursday.
He said that investigations were ongoing and that no arrests had been made.
A Plaid Cymru spokeswoman said: "Neil McEvoy has now been the subject of two break-ins, one at home and one at his office.
"Plaid Cymru is supporting him and his staff at this time and is keen that the police establish whether these intrusions are linked.
"All elected representatives and their staff deserve to operate in a democratic way without fear of harassment or intimidation.
"The National Assembly is working with Neil and his staff to ensure their safety and security, and we strongly urge that this continues."â€Ž

Perry Beeches III is one of a chain of six free schools. Mr Cameron described the schools as "a real success story".
But the Ofsted report said too many students were underachieving and described teaching as "inadequate".
Perry Beeches chief executive Liam Nolan said he "fundamentally disagreed" with the inspectors.
The school's headteacher, Darren Foreman, its senior leadership team and chair of governors have resigned, Mr Nolan said.
Mr Nolan has taken on the role of interim head teacher, together with Jackie Powell.
The report said: "Teaching is inadequate. Too much is dull and fails to engage students who became bored and start to fidget."
It also accused the school's leadership of having an, "unrealistic and inaccurate" view of the school and added students' behaviour required improvement.
Mr Nolan said: "This judgement makes me question Ofsted's credibility."
However he said he intended to work with Ofsted to make the school outstanding.
He described the report as an, "unfortunate blip".
He said: "Within six months you will see us back on the top."
The Perry Beeches schools are funded by central government but not run by local authorities.
Two of the other schools in the chain have been rated "outstanding" by Ofsted.
Perry Beeches III was opened by the Prime Minister in September 2013.
At the time, he said the majority of free schools were, "a real success story we should build on as a country".
A Department for Education spokesman said: "Liam Nolan and the Perry Beeches free schools are transforming the life chances of children in Birmingham, in some of the most deprived communities of the country.
"The performance of Perry Beeches I and II has set the bar for schools across the rest of the country.
"Swift action has already been taken to change the leadership of Perry Beeches III and to turn around the performance of the school."
A Plaid Cymru AM has claimed he has been a victim of "political harassment" after a break-in at his constituency office in Cardiff.
[NEXT_CONCEPT]
A £7m Birmingham free school opened by Prime Minister David Cameron is to go into special measures following a highly critical Ofsted report.