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 the custom field provided by ictime to log work as part of workflow transition screens (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).
This option is available since ictime 4.0.4. Previous versions do not support using the JIRA REST API.
Please have a look at the following example:
{ "update": { "comment": [ { "add": { "body": "." } } ] }, "fields": { "customfield_10100":"charged==on||timeSpentCorrected==1h||adjustEstimate==new||newEstimate==5w||activity==3||startDate==Sep 29, 2014 9:34 AM||startTime==5:05 PM||endTime==5:07 PM||comment==Bug has been fixed3||issueKey==ICJP-239||logWorkOption==summary||timeLogged==3w||", "assignee": { "name": "bob" }, "resolution": { "name": "Fixed" } }, "transition": { "id": "5" } }