At this moment, ictime does not offer any of it's functionality or data via an API. It is planned to offer selected functionality and data as part of a separate add-on until end of 2014.
ictime Custom Log Work Field & JIRA API
As this field (Custom Log Work Field) is logically a part of JIRA, you can use the JIRA REST API (https://developer.atlassian.com/display/JIRADEV/JIRA+REST+APIs) to work with this field (e.g. to log work as kind of API-driven, automated workflow transitions).