You could try:
String testString = 'Account.example__c';
List<String> splitString = testString.split('\\.');
Schema.SobjectField theField = Schema.getGlobalDescribe().get(splitString[0]).getDescribe().fields.getMap().get(splitString[1]);
This obviously has no error handling in it, but hopefully it gets you started.
Or breaking this down to understand it:
String testString = 'Account.example__c';
List<String> splitString = testString.split('\\.');
// store the object/field names
String objectName = splitString[0];
String fieldName = splitString[1];
// get the SObjectType
Schema.SObjectType objectType = Schema.getGlobalDescribe().get(objectName);
// get the fields on the object
Map<String, SObjectField> fieldMap = objectType.getDescribe().fields.getMap();
// The key to the map is the api name of the field
Schema.SobjectField theField = fieldMap.get(fieldName);