The 26-year-old told the Scottish Daily Mail that he was turned down for the job with the North Glasgow Universities Hospitals Trust in March.
Dr Everett Julyan says he was told he could not have the post of house officer with a Glasgow trust because he told interviewers that he would have nothing to do with training which involved terminations.
And on Saturday a spokesman for North Glasgow Universities Trust said: "We will investigate the interview process in this particular case to see why Dr Julyan was not given a job.
"The trust is an Equal Opportunities employer so we have to investigate claims of this nature."
Dr Julyan now works for South Glasgow Universities Hospitals Trust at the city's Southern General Hospital.
The 26-year-old told the Scottish Daily Mail that he was turned down for the job with the North Glasgow
Universities Hospitals Trust in March.
Like all junior doctors, Dr Julyan has to complete training as a house officer rotating through various hospital departments - including gynaecology.
He said he was asked at the interview if he would ever "clerk a patient in for an abortion" - a process which involves taking the patient's history and doing an examination.
He replied: "No."
Dr Julyan said: "I was called the next day and told I hadn't got the job because of that answer.
'Discrimination' claim
"I was utterly devastated. My wife was in tears, I was distraught."
He told the newspaper: "The difference with this case is that discrimination has never been verbally acknowledged before.
"If you don't get a job there is no onus on the employer to say why. But they volunteered the information."
Dr Julyan said that he wanted to do a rotation in gynaecology because much of a general practitioner's work is in that field.
'Deeply distressing'
"Without a grounding in gynaecology, I would be inadequately equipped to look after my patients and serve the public," he said.
"Given my views I find it deeply distressing that anyone should suggest being a gynaecologist requires conducting abortions."
He said he had decided to go public with his allegations to stop other doctors being discriminated against in the same way.
The hospital trust was at the centre of controversy earlier this year when Scotland's only heart surgeon resigned from the transplant unit it runs at Glasgow Royal Infirmary.