word(PROMISE)
 be under/on oath
to have formally promised to tell the truth: 已宣誓要讲真话
The judge reminded the witness that she was under oath.法官提醒证人她宣过誓要据实作证。

SMART Vocabulary: related words and phrases

Making & breaking promises & commitments
be on your honouridiom
bond
breach of contract
commit someone to something
commitment
committed
covenant
cross my heart (and hope to die)idiom
deliver on something
fink
fink out
pact
pledge
promises, promises!idiom
promisor
promissory
repledge
restrictive covenant
sworn
vow

You can also find related words, phrases, and synonyms in the topics:

Court cases, orders & decisions

oathnoun[C] (SWEAR WORD)

old-fashioned
an offensive word, especially one that uses a name for God: （尤指提及神灵的）诅咒，咒骂
muttering/mouthing oaths低声／默默地咒骂

SMART Vocabulary: related words and phrases

Swearing and blasphemy
blasphemous
blasphemously
blasphemy
C-word
curse
curse someone/yourself for something/doing something
damn
effing
four-letter word
profane
strong languagephrase
swear jar
swear word
swearing
sweary
sworn
the air is blueidiom
turn the air blueidiom
wash
wash your mouth out (with soap/soapy water)idiom

oath | American Dictionary

oath
noun[ C ]
us/oʊθ/

oathnoun[C] (PROMISE)

a serious promise that you will tell the truth or that you will do what you have said:
Presidents take an oath to uphold the Constitution.

oathnoun[C] (RUDE WORD)

literature dated
an offensive word, esp. one that uses a name for God

oath | Business English

oath
noun[ C ]
uk /əʊθ/us
an official promise, especially when you promise to tell the truth in court:
The witness took the oath.
A psychologist cannot be compelled to attend a disciplinary hearing or to swear on oath.
 on/under oath
LAW
having officially promised to tell the truth in court:
She was called to testify under oath before a congressional panel.
 take the oath of office
GOVERNMENT
to accept a job in a government, especially in the US, in a ceremony which requires you to make an official promise to serve your country:
The newly-elected Democrat took the oath of office in the Senate yesterday and quickly introduced his first bill.