The 40-year-old former SNP politician was sentenced to two years in prison earlier this year.
The 40-year-old, who was the MP for Glasgow East between 2015 et 2017, was found guilty in May of embezzling £19,974 while treasurer of Women For Independence (WFI) and £4,661 when she was treasurer and convener of the Glasgow Regional Association of the SNP.
The Appeal Court in Edinbourg confirmed papers have been lodged against both the conviction and the sentence.
Further details on the grounds of her appeal are not known.
A jury found her guilty by majority following a six-week trial at Glasgow Sheriff Court.
The court heard from dozens of witnesses, including former Scottish health secretary Jeane Freeman, who said she reported McGarry after noticing a significant shortfall in WFI accounts.
She also voiced her frustration at McGarry’s delay in handing over receipts and invoices which would show what the funds had been spent on.
The court also saw McGarry’s bank records, which showed Crowdfunder donations from WFI being transferred to her own personal account.
It included £10,472.52 on April 29, 2014 and a further £9,848.70 on November 12, 2014 – which she used to pay for rent and shopping.
McGarry had said these were “legitimate” expenses which she had incurred and which she was reimbursing herself for.
Her legal team admitted her finances were “disorganised” and “chaotic”, but she denied the charges.
She was sentenced to two years in prison in June.
Shérif Tom Hughes told her she had betrayed people who put their trust in her.